CRC RevEng

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Catalogue of parametrised CRC algorithms with 15 or fewer bits

CRC-3/GSM

width=3 poly=0x3 init=0x0 refin=false refout=false xorout=0x7 check=0x4 residue=0x2 name="CRC-3/GSM"

• Class: academic
• ETSI TS 100 909 version 8.9.0 (January 2005)
  • I Full mathematical description (Section 3.1.2.1, p.18 — Section 3.2.1, p.20)
• Created: 17 February 2017

CRC-3/ROHC

width=3 poly=0x3 init=0x7 refin=true refout=true xorout=0x0 check=0x6 residue=0x0 name="CRC-3/ROHC"

• Class: academic
• IETF RFC 3095 (July 2001)
  • I Definition: Width, Poly, Init (Section 5.9.2, pp.125–6)
• Andreas Vernersson et al. (26 May 2003), rohc 1.0 module rohc-1.0/rohc/src/c_util.c
  • III Code: C
• Created: 14 December 2009
• Updated: 4 August 2023

CRC-4/G-704

width=4 poly=0x3 init=0x0 refin=true refout=true xorout=0x0 check=0x7 residue=0x0 name="CRC-4/G-704"

• Class: academic
• Alias: CRC-4/ITU
• ITU-T Recommendation G.704 (October 1998)
  • I Full mathematical description (Section 2.3.3.5, p.12)
  • I Shift register diagram (Annex A.3, p.36)
• Created: 7 October 2008
• Updated: 21 November 2018

CRC-4/INTERLAKEN

width=4 poly=0x3 init=0xf refin=false refout=false xorout=0xf check=0xb residue=0x2 name="CRC-4/INTERLAKEN"

• Class: academic
• Reference from named polynomial in Prof. Koopman's CRC Polynomial Zoo.
• The Interlaken Alliance (7 October 2008), Interlaken Protocol Definition, version 1.2
  • I Definition: Width, Poly (Section 5.3.4.2, p.23)
  • I Definition: Init, RefIn, RefOut, XorOut (Appendix B, p.48)
• Created: 10 February 2016
• Updated: 4 August 2023

CRC-5/EPC-C1G2

width=5 poly=0x09 init=0x09 refin=false refout=false xorout=0x00 check=0x00 residue=0x00 name="CRC-5/EPC-C1G2"

• Class: attested
• Alias: CRC-5/EPC
• Used in standardised RFID tags.
• EPCglobal Inc™ (4 September 2018), EPC UHF Gen2 Air Interface Protocol: EPC™ Radio-Frequency Identity Protocols Generation-2 UHF RFID Standard, release 2.1
  • I Definition: Width, Poly, Init, Residue (Table 6-12, p.34)
  • I Definition: RefIn, Residue (Annex F.1, p.143)
  • I Shift register circuit diagram (Figure F-1, p.143)
  • I Transmission order, implying RefIn and RefOut (Section 6.3.1.4, p.33)
• Hee-Bok Kang et al. (December 2008), High Security FeRAM-Based EPC C1G2 UHF (860 MHz-960 MHz) Passive RFID Tag Chip, ETRI Journal, Volume 30 Number 6
  • IV 1 codeword (p.830)
    • 10001001​00000010​000110
• "jgmh" (20 May 2009), Computer Interfacing Forum topic 1330 (courtesy of the Internet Archive)
  • IV 1 codeword
    • 10000001​00000000​010011
• Created: 20 May 2009
• Updated: 28 December 2019

CRC-5/G-704

width=5 poly=0x15 init=0x00 refin=true refout=true xorout=0x00 check=0x07 residue=0x00 name="CRC-5/G-704"

• Class: academic
• Alias: CRC-5/ITU
• ITU-T Recommendation G.704 (October 1998)
  • I Definition: Residue; full mathematical description (Section 2.2.3.2, pp.8–9)
  • I Shift register diagram (Annex A.2, p.36)
• Created: 7 October 2008
• Updated: 21 November 2018

CRC-5/USB

width=5 poly=0x05 init=0x1f refin=true refout=true xorout=0x1f check=0x19 residue=0x06 name="CRC-5/USB"

• Class: confirmed
• Cypress Semiconductor Corporation (26 July 2001), SL811HS/SL811HST Application Notes, Revision 1.21 (courtesy of Stardot.org.uk Forums)
  • II Transcript confirming implementation with 4 codewords (pp.25,30)
    • 00000000​00001000
    • 10000000​10000011
    • 00101110​00011000
    • 10101110​00000111
• Anonymous (10 July 1997), "Cyclic Redundancy Checks in USB" (Draft) (courtesy of the Internet Archive)
  • III Definition: Width, Poly, Init, XorOut (p.2)
  • III Definition: Residue (p.3)
  • III Code: Perl (pp.3–4)
  • IV 4 codewords (p.5)
    • 10101000​11110111
    • 01011100​10111100
    • 00001110​01001110
    • 10000000​00010111
• Created: 1 December 2007
• Updated: 12 July 2024

CRC-6/CDMA2000-A

width=6 poly=0x27 init=0x3f refin=false refout=false xorout=0x00 check=0x0d residue=0x00 name="CRC-6/CDMA2000-A"

• Class: attested
• 3rd Generation Partnership Project 2 (3GPP2) (September 2009), Physical layer standard for cdma2000 spread spectrum systems, revision E, version 1.0 (courtesy of the Internet Archive)
  • I Definition: Width, Poly (Section 2.1.3.1.4.1.5, p.2-97)
  • I Full description (Section 2.1.3.1.4.1, p.2-95)
  • I Shift register diagram (Figure 2.1.3.1.4.1.5-1, p.2-97)
• Agilent Technologies, Advanced Design System 2008 Update 2, CDMA2K_CRC_Coder module documentation (courtesy of the Internet Archive)
  • III Full description
• J. Hurley, Avtec Inc. (6 May 2011), Computer Interfacing Forum topic 1702 (courtesy of the Internet Archive)
  • IV 3 codewords
    • C101002E
    • 0110000F
    • 05100009
• reveng -m CRC-6/CDMA2000-A -a 1 -A 6 -X -c 11000001​00000001​00000000​00 00000001​00010000​00000000​00 00000101​00010000​00000000​00 → 2E 0F 09
• Created: 14 October 2013
• Updated: 28 July 2023

CRC-6/CDMA2000-B

width=6 poly=0x07 init=0x3f refin=false refout=false xorout=0x00 check=0x3b residue=0x00 name="CRC-6/CDMA2000-B"

• Class: academic
• 3rd Generation Partnership Project 2 (3GPP2) (September 2009), Physical layer standard for cdma2000 spread spectrum systems, revision E, version 1.0 (courtesy of the Internet Archive)
  • I Definition: Width, Poly (Section 2.1.3.1.4.1.6, pp.2-97–8)
  • I Full description (Section 2.1.3.1.4.1, p.2-95)
  • I Shift register diagram (Figure 2.1.3.1.4.1.6-1, p.2-98)
• Agilent Technologies, Advanced Design System 2008 Update 2, CDMA2K_CRC_Coder module documentation (courtesy of the Internet Archive)
  • III Full description
• Created: 14 October 2013
• Updated: 28 July 2023

CRC-6/DARC

width=6 poly=0x19 init=0x00 refin=true refout=true xorout=0x00 check=0x26 residue=0x00 name="CRC-6/DARC"

• Class: attested
• ETSI EN 300 751 version 1.2.1 (January 2003)
  • I Definition: Width, Poly (Section 11.2, pp.67–8)
  • I Definition: RefIn, RefOut (Section 12, pp.69–70)
  • IV 3 codewords (Section 11.2, pp.67–8)
    • 10010100​11000100
    • 01010011​00011101
    • 00001100​01000000​00100000​00101101
  • See section 12 for details of the transmission order.
• reveng -m CRC-6/DARC -X -c 2923 CAB8 300204B4 → 00 00 00
• reveng -m CRC-6/DARC -a 1 -A 8 -r -X -c 10010100​11 01010011​00 00001100​01000000​00100000​00 → 20 B8 B4
• Unique effective solution of codeword set
• Created: 14 December 2009
• Updated: 20 November 2018

CRC-6/G-704

width=6 poly=0x03 init=0x00 refin=true refout=true xorout=0x00 check=0x06 residue=0x00 name="CRC-6/G-704"

• Class: academic
• Alias: CRC-6/ITU
• ITU-T Recommendation G.704 (October 1998)
  • I Full mathematical description (Section 2.1.3.1.2, p.3)
  • I Shift register diagram (Annex A.1, p.35)
• Created: 7 October 2008
• Updated: 21 November 2018

CRC-6/GSM

width=6 poly=0x2f init=0x00 refin=false refout=false xorout=0x3f check=0x13 residue=0x3a name="CRC-6/GSM"

• Class: academic
• ETSI TS 100 909 version 8.9.0 (January 2005)
  • I Full mathematical description (Section 3.9.4.3, pp.31–3 — Section 3.10.7.3, pp.47–9 — Section 4.6, p.64 — Section 5.3.2, p.95)
• Created: 17 February 2017

CRC-7/MMC

width=7 poly=0x09 init=0x00 refin=false refout=false xorout=0x00 check=0x75 residue=0x00 name="CRC-7/MMC"

• Class: academic
• Alias: CRC-7
• Used in the MultiMediaCard interface.
• Additional reference courtesy of Greg Nelson, Grammatech Inc.
• JEDEC Standard JESD84-A441 (March 2010) (registration required)
  • I Full definition (Section 10.2, pp.157–8)
  • I Shift register diagram (Figure 53, p.158)
• Linux contributors (14 January 2021), Linux module lib/crc7.c
  • III Code: C
• Nokia Corporation (2008), Linux module drivers/net/wireless/ti/wl1251/spi.c
  • III Definition: Init (l.104)
• Created: 7 October 2008
• Updated: 11 January 2022

CRC-7/ROHC

width=7 poly=0x4f init=0x7f refin=true refout=true xorout=0x00 check=0x53 residue=0x00 name="CRC-7/ROHC"

• Class: academic
• IETF RFC 3095 (July 2001)
  • I Definition: Width, Poly, Init (Section 5.9.2, pp.125–6)
• Andreas Vernersson et al. (26 May 2003), rohc 1.0 module rohc-1.0/rohc/src/c_util.c
  • III Code: C
• Created: 14 December 2009
• Updated: 4 August 2023

CRC-7/UMTS

width=7 poly=0x45 init=0x00 refin=false refout=false xorout=0x00 check=0x61 residue=0x00 name="CRC-7/UMTS"

• Class: academic
• Reference from named polynomial in Prof. Koopman's CRC Polynomial Zoo.
• 3rd Generation Partnership Project (3GPP) TS 25.427 version 17.0.0 (April 2022) (zipped MS Word document) — ETSI TS 125 427 version 17.0.0 (April 2022)
  • I Definition: Width, Poly, Init, XorOut (Section 7.2.1, p.40)
  • I Definition: RefIn, RefOut (Section 6.1.1, p.20; Section 7.2.1.1, pp.40–1)
• Created: 8 February 2016
• Updated: 7 May 2022

CRC-8/AUTOSAR

width=8 poly=0x2f init=0xff refin=false refout=false xorout=0xff check=0xdf residue=0x42 name="CRC-8/AUTOSAR"

• Class: attested
• AUTOSAR (24 November 2022), AUTOSAR Classic Platform release R22-11, Specification of CRC Routines
  • I Comprehensive primer on CRC theory (Section 7.1, pp.19–22)
  • I All parameters (Section 7.2.1.2, p.25)
  • IV 7 codewords (Section 7.2.1.2, p.25)
    • 00000000​12
    • F20183C2
    • 0FAA0055​C6
    • 00FF5511​77
    • 332255AA​BBCCDDEE​FF11
    • 926B5533
    • FFFFFFFF​6C
• Unique effective solution of codeword set
• Created: 24 July 2016
• Updated: 28 July 2023

CRC-8/BLUETOOTH

width=8 poly=0xa7 init=0x00 refin=true refout=true xorout=0x00 check=0x26 residue=0x00 name="CRC-8/BLUETOOTH"

• Class: attested
• Used in Bluetooth header error correction (HEC). Init=0x00 is used in the Inquiry Response substate.
• Bluetooth SIG (31 January 2023), Bluetooth Specification, Core Version 5.4
  • I Definition: Init (Section 2.B.1.2.1, p.425; Section 2.B.6.4.6, p.478 — Section 2.B.6.5.1.4, pp.481–3 — Section 2.B.7.1, p.497 — Section 2.B.8.4.3, pp.525–7)
  • I Definition: Width, Poly (Section 2.B.7.1.1, pp.497–8)
  • I Definition: RefIn; shift register diagram (Figure 2.B.7.3, p.498)
  • I Definition: Refin, RefOut, Residue (Figure 2.B.7.5, p.498)
  • IV 10 codewords (Section 2.G.4, p.899)
    • 11000100​10100001​11
    • 00100100​10010011​00
    • 10100100​10010110​10
    • 01100100​10010001​11
    • 11100100​10010100​01
    • 11011000​10011110​01
    • 00111000​10101100​10
    • 10111000​10101001​00
    • 01111000​10101110​01
    • 11111000​10101011​11
• Created: 20 June 2017
• Updated: 29 July 2023

CRC-8/CDMA2000

width=8 poly=0x9b init=0xff refin=false refout=false xorout=0x00 check=0xda residue=0x00 name="CRC-8/CDMA2000"

• Class: academic
• 3rd Generation Partnership Project 2 (3GPP2) (September 2009), Physical layer standard for cdma2000 spread spectrum systems, revision E, version 1.0 (courtesy of the Internet Archive)
  • I Definition: Width, Poly (Section 2.1.3.1.4.1.4, p.2-96)
  • I Full description (Section 2.1.3.1.4.1, p.2-95)
  • I Shift register diagram (Figure 2.1.3.1.4.1.4-1, p.2-97)
• Agilent Technologies, Advanced Design System 2008 Update 2, CDMA2K_CRC_Coder module documentation (courtesy of the Internet Archive)
  • III Full description
• Created: 14 October 2013
• Updated: 28 July 2023

CRC-8/DARC

width=8 poly=0x39 init=0x00 refin=true refout=true xorout=0x00 check=0x15 residue=0x00 name="CRC-8/DARC"

• Class: attested
• The single codeword is supported by the codewords confirming CRC-6/DARC, defined identically apart from Poly in the same standard.
• ETSI EN 300 751 version 1.2.1 (January 2003)
  • I Definition: Width, Poly (Section 11.2.3, p.68)
  • I Definition: RefIn, RefOut (Section 12, pp.69–70)
  • IV 1 codeword (Section 11.2.3, p.68)
    • 00000001​00000011​11010111
  • See section 12 for details of the transmission order.
• Created: 14 December 2009
• Updated: 29 November 2018

CRC-8/DVB-S2

width=8 poly=0xd5 init=0x00 refin=false refout=false xorout=0x00 check=0xbc residue=0x00 name="CRC-8/DVB-S2"

• Class: academic
• Contributed by Hartmut Brandt, German Aerospace Center.
• ETSI EN 302 307-1 version 1.4.1 (November 2014)
  • I Full mathematical description (Section 5.1.4, p.18)
• ETSI EN 302 755 version 1.4.1 (July 2015)
  • I Full mathematical description (Annex F, p.163)
• Ethernet POWERLINK Standardisation Group (18 October 2018), OpenSAFETY Safety Profile Specification Working Draft Proposal, version 1.5.2
  • I Code: C (Appendix 1, pp.196–9)
  • IV 1 codeword (Appendix 1, l.3522, p.197)
    • 22C81256​30112233​44556677​884F
• Prof. Philip Koopman, Tridib Chakravarty (June 2004), Cyclic Redundancy Code (CRC) Polynomial Selection for Embedded Networks
  • III Assessment of polynomial performance (as 0xEA or CRC-8)
• Created: 10 January 2014
• Updated: 29 July 2023

CRC-8/GSM-A

width=8 poly=0x1d init=0x00 refin=false refout=false xorout=0x00 check=0x37 residue=0x00 name="CRC-8/GSM-A"

• Class: academic
• ETSI TS 100 909 version 8.9.0 (January 2005)
  • I Full mathematical description (Section 3.1.1.1, pp.17–18)
• Michael Niedermayer, Aurélien Jacobs et al. (27 February 2023), FFmpeg 6.0 (XZ compressed tarfile), module ffmpeg-6.0/libavutil/tests/crc.c
  • IV 1 codeword
    • (i+i*i) × 1999 + D6
• Created: 17 February 2017
• Updated: 8 August 2024

CRC-8/GSM-B

width=8 poly=0x49 init=0x00 refin=false refout=false xorout=0xff check=0x94 residue=0x53 name="CRC-8/GSM-B"

• Class: academic
• ETSI TS 100 909 version 8.9.0 (January 2005)
  • I Full mathematical description (Section 5.1.5.1.3, p.71 — Section 5.1.5.2.2, p.73 — Section 5.1.9.1.3, p.80 — Section 5.1.9.2.2, p.83 — Section 5.1.11.1.3, pp.86–7 — Section 5.1.11.2.2, p.89)
• Created: 17 February 2017

CRC-8/HITAG

width=8 poly=0x1d init=0xff refin=false refout=false xorout=0x00 check=0xb4 residue=0x00 name="CRC-8/HITAG"

• Class: attested
• Contributed by Philippe Teuwen.
• Used in RFID applications.
• Philips Semiconductors (4 October 2001), HITAG core module hardware HTCM400 Product Specification (courtesy of Digi-Key Electronics)
  • I Definition: Width, Poly, Init (Section 7.6.1, p.10)
• Philips Semiconductors (18 July 2006), HTS IC H32/HTS IC H56/HTS IC H48 transponder IC Product Specification, revision 3.1 (courtesy of Digi-Key Electronics)
  • I Definition: Width, Poly, Init (Section 13.1, p.45 — Section 13.2.2, p.45)
  • I Code: C (Section 13.3, p.46)
  • IV 1 codeword (Section 13.3, p.46)
    • 00000001​01100011​01000000​01101101​10100100​11110 (source: 00000 + 2C680DB4​9E)
• "Sixkay" (July–August 2015), Proxmark3 community forum post
  • IV 1 codeword
    • CA9340FF​C6
• reveng -m CRC-8/HITAG -a 1 -A 8 -X -c 00000001​01100011​01000000​01101101​10100100​11110 11001010​10010011​01000000​11111111​11000110 → 00 00
• Created: 23 December 2021
• Updated: 4 August 2023

CRC-8/I-432-1

width=8 poly=0x07 init=0x00 refin=false refout=false xorout=0x55 check=0xa1 residue=0xac name="CRC-8/I-432-1"

• Class: academic
• Alias: CRC-8/ITU
• Used as the Asynchronous Transfer Mode Header Error Control sequence (ATM HEC). Single bit errors in the 4-byte ATM header can be automatically corrected.
• ITU-T Recommendation I.432.1 (February 1999)
  • I Full mathematical description (Section 7.3.2.2, p.5)
  • IV 2 trivial codewords (Section 7.3.2.2, p.6; Table 3, p.12)
    • 00000000​00000000​00000000​00000000​01010101
    • 00000000​00000000​00000000​00000001​01010010
• Broadband Forum Technical Committee (10 September 1993), User-Network Interface Specification, version 3.0 (compressed RTF) (courtesy of the Internet Archive)
  • I Full mathematical description (Section 2.2.6)
• Created: 19 April 2009
• Updated: 2 August 2023

CRC-8/I-CODE

width=8 poly=0x1d init=0xfd refin=false refout=false xorout=0x00 check=0x7e residue=0x00 name="CRC-8/I-CODE"

• Class: attested
• Philips Semiconductors (30 January 2004), SL2 ICS11 Product Specification, revision 3.0 (courtesy of the Internet Archive)
  • I Definition: Width, Poly, Init (Section 10.1, p.26)
  • I Code: C (Section 10.3.1, pp.27–9)
  • I Worked example (as code trace) (Section 10.3.1, p.29)
• Created: 3 November 2007
• Updated: 6 February 2017

CRC-8/LTE

width=8 poly=0x9b init=0x00 refin=false refout=false xorout=0x00 check=0xea residue=0x00 name="CRC-8/LTE"

• Class: academic
• Reference from named polynomial in Prof. Koopman's CRC Polynomial Zoo.
• 3rd Generation Partnership Project (3GPP) TS 36.212 version 17.1.0 (March 2022) (zipped MS Word document) — ETSI TS 136 212 version 17.1.0 (April 2022)
  • I Definition: Width, Poly, Init, XorOut, Residue (Section 5.1.1, pp.10–11)
  • I Attachment relation, defining RefIn ^ RefOut (Section 5.1.1, p.11)
• 3rd Generation Partnership Project (3GPP) TS 36.321 version 17.5.0 (June 2023) (zipped MS Word document) — ETSI TS 136 321 version 17.5.0 (July 2023)
  • Referenced from TS 136 212 section 5.2.2.1, p.26
  • I Definition: RefIn, RefOut (Section 6.1.1, p.90)
• Created: 13 February 2016
• Updated: 5 August 2023

CRC-8/MAXIM-DOW

width=8 poly=0x31 init=0x00 refin=true refout=true xorout=0x00 check=0xa1 residue=0x00 name="CRC-8/MAXIM-DOW"

• Class: attested
• Alias: CRC-8/MAXIM, DOW-CRC
• Used in Maxim 1-Wire® device registration numbers.
• Maxim Integrated (8 August 2012), DS1921G Datasheet
  • I Definition: Width, Poly, Init, XorOut (p.9)
  • I Shift register diagram (p.9)
• Maxim Integrated (22 August 2012), Application Note 27 (PDF, HTML)
  • I Definition: Init, Residue (pp.3–4)
  • I Shift register diagram (p.3)
  • I Code: 8051 assembler, Pascal (pp.5–8)
  • I Worked examples (pp.5–9)
• Maxim Integrated, Maxim iButton® datasheets (for links see Application Note 27)
  • IV 15 codewords
    • DS1904: 242BC5FB​00000040 (source: 40000000​FBC52B24)
    • DS1920: 102BC5FB​000000A0 (source: A0000000​FBC52B10)
    • DS1921G: 212BC5FB​00000089 (source: 89000000​FBC52B21)
    • DS1971: 142BC5FB​00000054 (source: 54000000​FBC52B14)
    • DS1971: 14B3D8FB​000000D4 (source: D4000000​FBD8B314)
    • DS1973: 232BC5FB​000000F3 (source: F3000000​FBC52B23)
    • DS1973: 23B3D8FB​00000073 (source: 73000000​FBD8B323)
    • DS1982: 092BC5FB​00000097 (source: 97000000​FBC52B09)
    • DS1982: 09B3D8FB​00000017 (source: 17000000​FBD8B309)
    • DS1985: 0B2BC5FB​000000ED (source: ED000000​FBC52B0B)
    • DS1985: 0BB3D8FB​0000006D (source: 6D000000​FBD8B30B)
    • DS1986: 0F2BC5FB​00000019 (source: 19000000​FBC52B0F)
    • DS1986: 0FB3D8FB​00000099 (source: 99000000​FBD8B30F)
    • DS1995: 0A2BC5FB​000000D0 (source: D0000000​FBC52B0A)
    • DS1996: 0C2BC5FB​0000005E (source: 5E000000​FBC52B0C)
• Created: 26 April 2009
• Updated: 2 January 2021

CRC-8/MIFARE-MAD

width=8 poly=0x1d init=0xc7 refin=false refout=false xorout=0x00 check=0x99 residue=0x00 name="CRC-8/MIFARE-MAD"

• Class: attested
• References courtesy of Sourceforge users "xavery" and Oleg Moiseenko.
• NXP Semiconductors (6 November 2018), Application note AN10787: MIFARE Application Directory (MAD), rev. 7.4
  • I Definition: Width, Poly, Init (Section 3.7, pp.9–10)
  • IV 1 codeword (Table 11, p.10)
    • 01010801​08010800​00000000​00040003​10031002​10021000​00000000​00113089
• Romain Tartière, Romuald Conty, et al. (29 June 2017), libfreefare module libfreefare/libfreefare/mad.c
  • III Code: C
• Romain Tartière (29 June 2017), libfreefare module libfreefare/test/test_mad.c
  • IV 3 codewords (1 same as in AN10787)
    • 0103E103​E103E103​E103E100​00000000​00000000​00000000​00000000​000000C4
    • 0103E103​E103E103​E103E103​E1000000​00000000​00000000​00000000​000000AB
• Oleg Moiseenko (14 February 2019), CRC RevEng project discussion thread post
  • IV 1 codeword
    • 00563D56​3C563C56​3C563C56​3C000000​00000000​00000000​00000000​00000030
• Created: 21 February 2019

CRC-8/NRSC-5

width=8 poly=0x31 init=0xff refin=false refout=false xorout=0x00 check=0xf7 residue=0x00 name="CRC-8/NRSC-5"

• Class: attested
• iBiquity Digital Corporation (16 December 2016), HD Radio™ Air Interface Design Description: Audio Transport, rev. H (courtesy of National Radio Systems Committee)
  • I Definition: Width, Poly (Section 5.2.3.2, p.33)
  • Incorporated by normative reference into National Radio Systems Committee standard NRSC-5-D.
• Andrew Wesie (9 June 2017), NRSC-5 receiver for rtl-sdr, file nrsc5/support/sample.xz (XZ compressed raw radio recording, 22 MB)
  • II Recording confirming implementation with 587 codewords (selection)
    • 5822EF63​9D240114​F25D007C​DA4208A1​CBBDE9DF​D73273A7​D1800030​38EB
    • B002F6E0​1BF5E00B​E3F6D054​50D23B70​273990D9​0ED77AED​F6EB803C​1AD30A68​5E0A009A
    • 412C5659​98C49382​14C58005​800B09CA​BACB98B6​56DE98FB​199A1892​3DE06D59​2D2D399A​5CA72CFA​D96BC107​35E4774F​A06AFEAB​1726EF0F​471ABED7​04DA798D​EDABB16D​1A4F0D7B​7C49F65C​1EBE2D5D​E6EB16D8​BF2DB019​9F76D6C8​455C1C70​251B4290​CA669C00​AC529FC0​01400217​4006E686​0558EEF5​CBE4DEF9​94D1F642​156E48FA​68072E78​A7F1C88A​80DF0251​6B5672FF​F281780B​6200A3
    • 896C6088​52750D2D​C9249055​5A448BA6​55686F62​F35A2F75​22C62EB1​31618814​68600683​310689
    • 412C5700​68CB2362​DCCB2400​004416B4​2A5F9B2C​469A721D​106258A7​6D77C2F1​05C315DA​1257CAD1​232A4728​2475FB25​0171BCC0​94DE3C57​11A0B688​92F7A568​5CAB9788​1BFA8020​56600688​A08815EA​D3C069B6​8A952C00​058BD007​1DFD5F97​5D1CFD97​6FAE0A82​A1AF1636​E4687EE4​72C62F22​A96E3197​B8894385​2B128D04​89E911B8​5B840231​22176D06​70130348​DDD55441​6BB8852A​854364
    • 0D0640C6​D800124B
    • 89866AD8​12A05E80​34A3BBBA​AAB56AD4​FAD9894B​00300000​00007752
• Andrew Wesie, Clayton Smith et al. (25 October 2017), NRSC-5 receiver for rtl-sdr, module nrsc5/src/frame.c
  • III Code: C
• Unique effective solution of codeword set
• Created: 16 November 2018
• Updated: 20 March 2019

CRC-8/OPENSAFETY

width=8 poly=0x2f init=0x00 refin=false refout=false xorout=0x00 check=0x3e residue=0x00 name="CRC-8/OPENSAFETY"

• Class: attested
• Ethernet POWERLINK Standardisation Group (18 October 2018), OpenSAFETY Safety Profile Specification Working Draft Proposal, version 1.5.2
  • I Full description (Section 5.1.2.6, pp.43–4)
  • I Error detection capability (Section 8.1, p.182)
  • I Code: C (Appendix 1, pp.196–9)
  • IV 1 codeword (Appendix 1, l.3519, pp.196–7)
    • 23C80834​11223344​55667788​3C
• Roland Knall (6 February 2012), openSAFETY communication using Ethernet Powerlink V2 as transport protocol (PCAP file) (courtesy of Wireshark Wiki)
  • II Transcript confirming implementation (selected codewords)
    • 02A80600​00606500​06A11C
    • 03A80001​00006065​0006A131
    • 03A80600​00606500​07211D
    • 02A80001​00006065​0007211D
    • 04A80600​00606500​021393
    • 05A80001​00006065​00021350
    • 01AC0600​00606500​0721AF
    • 00AC0003​00006065​000721B5
• Prof. Philip Koopman, Tridib Chakravarty (June 2004), Cyclic Redundancy Code (CRC) Polynomial Selection for Embedded Networks
  • III Assessment of polynomial performance (as 0x97 or C₂)
• Unique effective solution of codeword set
• Created: 22 July 2016
• Updated: 7 May 2022

CRC-8/ROHC

width=8 poly=0x07 init=0xff refin=true refout=true xorout=0x00 check=0xd0 residue=0x00 name="CRC-8/ROHC"

• Class: academic
• IETF RFC 3095 (July 2001)
  • I Definition: Width, Poly, Init, XorOut (Section 5.9.1, p.125)
• Andreas Vernersson et al. (26 May 2003), rohc 1.0 module rohc-1.0/rohc/src/c_util.c
  • III Code: C
• Created: 14 December 2009
• Updated: 4 August 2023

CRC-8/SAE-J1850

width=8 poly=0x1d init=0xff refin=false refout=false xorout=0xff check=0x4b residue=0xc4 name="CRC-8/SAE-J1850"

• Class: attested
• SAE Standard J1850 (15 May 1994), Excerpt (courtesy of the Internet Archive)
  • I Definition: Width, Poly, Init, XorOut, Residue (Section 5.4.1, p.14)
  • IV 7 codewords (Table 1, p.15)
    • 00000000​59
    • F2018337
    • 0FAA0055​79
    • 00FF5511​B8
    • 332255AA​BBCCDDEE​FFCB
    • 926B558C
    • FFFFFFFF​74
• AUTOSAR (24 November 2022), AUTOSAR Classic Platform release R22-11, Specification of CRC Routines
  • I Comprehensive primer on CRC theory (Section 7.1, pp.19–22)
  • I All parameters (Section 7.2.1.1, p.24)
  • IV 7 codewords (same as in SAE Standard J1850) (Section 7.2.1.1, pp.24–5)
• "knivmannen" (24 May 2010), StackOverflow submitted question
  • IV 5 codewords
    • 55FF0000​ECFF601F
    • 55FF0000​F0FFA038
    • 660BEAFF​BFFFC0CA
    • 5E18EAFF​B7FF60BD
    • F6301600​FCFE1081
• Unique effective solution of codeword set
• Created: 17 February 2016
• Updated: 3 August 2023

CRC-8/SMBUS

width=8 poly=0x07 init=0x00 refin=false refout=false xorout=0x00 check=0xf4 residue=0x00 name="CRC-8/SMBUS"

• Class: attested
• Alias: CRC-8
• The System Management Interface Forum, Inc. (3 August 2000), System Management Bus (SMBus) Specification, version 2.0 (courtesy of the Internet Archive)
  • I Definition: Width, Poly, RefIn, RefOut (Section 4.2, p.19; Section 5.4.1.3, p.27)
• The System Management Interface Forum, Inc. (14 June 2005), CRC-8 Calculator
  • II Implementation
• PVL Team (25 October 2008), CRC .NET control, version 14.0.0.0
  • II Implementation
• John Milios, USAR Systems, Inc. (22 April 1999), Firmware CRC-8 implementations for SMBus (courtesy of the Internet Archive)
  • III Definition: Width, Poly (p.5)
  • III Worked example (p.6)
  • III Code: 6805 assembler (pp.14,18)
• Michael Niedermayer, Aurélien Jacobs et al. (27 February 2023), FFmpeg 6.0 (XZ compressed tarfile), module ffmpeg-6.0/libavutil/tests/crc.c
  • IV 1 codeword
    • (i+i*i) × 1999 + E3
• Created: 30 March 2005
• Updated: 8 August 2024

CRC-8/TECH-3250

width=8 poly=0x1d init=0xff refin=true refout=true xorout=0x00 check=0x97 residue=0x00 name="CRC-8/TECH-3250"

• Class: attested
• Alias: CRC-8/AES, CRC-8/EBU
• Reference from StackOverflow question by "ZeroDefect" (18 June 2012)
• European Broadcasting Union (8 June 2004), Tech 3250: Specification of the digital audio interface, 3rd edition
  • I Definition: Width, Poly, Init (Section 4, p.12)
  • I Shift register diagrams (Appendix 1, p.17)
  • IV 2 codewords (Appendix 1, pp.17–18)
    • 3D020000​02000000​00000000​00000000​00000000​0000009B
    • 01000000​00000000​00000000​00000000​00000000​00000032
• Created: 19 July 2012
• Updated: 21 November 2018

CRC-8/WCDMA

width=8 poly=0x9b init=0x00 refin=true refout=true xorout=0x00 check=0x25 residue=0x00 name="CRC-8/WCDMA"

• Class: third-party
• Andrew Richardson (17 March 2005), WCDMA Design Handbook, Cambridge University Press, ISBN 0-521-82815-5 (embedded content)
  • III Definition: Width, Poly, Residue (Section 7.1.3, Table 7.3, p.223)
  • III Shift register diagram (Figure 7.4, p.223)
• Prof. Philip Koopman, Tridib Chakravarty (June 2004), Cyclic Redundancy Code (CRC) Polynomial Selection for Embedded Networks
  • III Assessment of polynomial performance (as 0xCD or WCDMA-8)
• "Max" (26 October 2009), Computer Interfacing Forum topic 1431 (courtesy of the Internet Archive)
  • IV 46 codewords (selection)
    • 00001148
    • 00012077
    • 80800012
    • 00001021​01002200​0A002D00​00000000​00460A20
    • 00001021​01012300​0A002800​00000000​00460A54
    • 00001021​01012500​0A002900​00000000​00460A4B
    • 40001020​0B01001A​000A0001​00000000​00800900​1F01F393
    • 40001020​0B01001F​000A0001​00000000​00000900​1F01F3F7
    • 40001020​0B010020​000A0001​00000000​00000900​1F01F331
    • 40001107​083829B4​1903
    • 40001107​08482668​2180
    • 40001107​085C2934​17A8
  • IV 1 non-matching codeword
    • 00001268 ≠ …8B
• Unique effective solution of codeword set
• Created: 8 November 2009
• Updated: 28 December 2019

CRC-10/ATM

width=10 poly=0x233 init=0x000 refin=false refout=false xorout=0x000 check=0x199 residue=0x000 name="CRC-10/ATM"

• Class: attested
• Alias: CRC-10, CRC-10/I-610
• Used in Asynchronous Transfer Mode AAL 3/4 and OAM cells. Note there are 6 padding zero bits between each of the 46-byte information fields and their respective CRCs.
• ITU-T Recommendation I.610 (February 1999)
  • I Full mathematical description (Section 10.1, p.40)
  • IV 2 codewords (Appendix I, p.67)
    • 116A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A00AF
    • 1801AAAA​AAAAFFFF​FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFF6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A02AC
• Broadband Forum Technical Committee (March 1999), Traffic Management Specification, version 2.1 (courtesy of the Internet Archive)
  • I Full mathematical description (Section 5.10.3.1, p.47)
• Charles M. Heard, Generating and Checking CRC-10 in ATM AAL 3/4 or OAM Cells (courtesy of the Internet Archive)
  • III Definition: Width, Poly
  • III Code: C
  • IV 7 codewords (selection; first four attributed to Angie Tso, Telecommunications Techniques Corp.)
    • 0A0B0C0D​0E0F0000​00000000​00000000​00000000​00000000​00000000​00000000​00000000​00000000​00000000​000001F6
    • 11111111​11111111​11110000​00000000​00000000​00000000​00000000​00000000​00000000​00000000​00000000​0000016B
    • FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFF030F
    • 12345678​90123456​78901234​56789012​34567890​12345678​90123456​78901234​56789012​34567890​12345678​901202ED
    • 106A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A6A6A​6A6A03B9
    • 18010000​0000FFFF​FFFFFFFF​FFFFFFFF​FFFFFFFF​FFFF0000​00000000​00000000​00000000​00006A6A​6A6A6A6A​6A6A004A
• Created: 19 April 2009
• Updated: 7 May 2022

CRC-10/CDMA2000

width=10 poly=0x3d9 init=0x3ff refin=false refout=false xorout=0x000 check=0x233 residue=0x000 name="CRC-10/CDMA2000"

• Class: academic
• 3rd Generation Partnership Project 2 (3GPP2) (September 2009), Physical layer standard for cdma2000 spread spectrum systems, revision E, version 1.0 (courtesy of the Internet Archive)
  • I Definition: Width, Poly (Section 2.1.3.1.4.1.3, p.2-96)
  • I Full description (Section 2.1.3.1.4.1, p.2-95)
  • I Shift register diagram (Figure 2.1.3.1.4.1.3-1, p.2-96)
• Agilent Technologies, Advanced Design System 2008 Update 2, CDMA2K_CRC_Coder module documentation (courtesy of the Internet Archive)
  • III Full description
• Created: 14 October 2013
• Updated: 28 July 2023

CRC-10/GSM

width=10 poly=0x175 init=0x000 refin=false refout=false xorout=0x3ff check=0x12a residue=0x0c6 name="CRC-10/GSM"

• Class: academic
• ETSI TS 100 909 version 8.9.0 (January 2005)
  • I Full mathematical description (Section 4.7, p.65)
• Created: 17 February 2017

CRC-11/FLEXRAY

width=11 poly=0x385 init=0x01a refin=false refout=false xorout=0x000 check=0x5a3 residue=0x000 name="CRC-11/FLEXRAY"

• Class: attested
• Alias: CRC-11
• FlexRay Consortium (October 2010), FlexRay Communications System Protocol Specification, version 3.0.1 (courtesy of nlrp Benchmark)
  • I Definition: Width, Poly, Init, RefOut (Section 4.2.8, pp.114–5)
  • I Pseudocode (Section 4.5, pp.118–9)
• FlexRay Consortium (October 2010), FlexRay Protocol Conformance Test Specification, version 3.0.1 (courtesy of nlrp Benchmark)
  • IV 1 codeword (Section 2.7.5, p.681)
    • 11000000​00010000​00010000​0100110
• Robert Bosch GmbH (3 December 2007), E-Ray FlexRay IP Module, Application Note 001: Wakeup (embedded content; courtesy of Yumpu)
  • IV 3 codewords (Section 4.4.3, pp.27–30; researched by Vivek Rajan)
    • 11000000​00001000​10000010​0011011
    • 11000000​00010000​10000110​0000100
    • 00000000​00011000​10001011​1010010
• Created: 3 November 2007
• Updated: 7 May 2022

CRC-11/UMTS

width=11 poly=0x307 init=0x000 refin=false refout=false xorout=0x000 check=0x061 residue=0x000 name="CRC-11/UMTS"

• Class: academic
• Reference from named polynomial in Prof. Koopman's CRC Polynomial Zoo.
• 3rd Generation Partnership Project (3GPP) TS 25.427 version 17.0.0 (April 2022) (zipped MS Word document) — ETSI TS 125 427 version 17.0.0 (April 2022)
  • I Definition: Width, Poly, Init, XorOut (Section 7.2.1, p.40)
  • I Definition: RefIn, RefOut (Section 6.1.1, p.20; Section 7.2.1.1, pp.40–1)
• Created: 8 February 2016
• Updated: 7 May 2022

CRC-12/CDMA2000

width=12 poly=0xf13 init=0xfff refin=false refout=false xorout=0x000 check=0xd4d residue=0x000 name="CRC-12/CDMA2000"

• Class: academic
• 3rd Generation Partnership Project 2 (3GPP2) (September 2009), Physical layer standard for cdma2000 spread spectrum systems, revision E, version 1.0 (courtesy of the Internet Archive)
  • I Definition: Width, Poly (Section 2.1.3.1.4.1.2, p.2-95)
  • I Full description (Section 2.1.3.1.4.1, p.2-95)
  • I Shift register diagram (Figure 2.1.3.1.4.1.2-1, p.2-96)
• Agilent Technologies, Advanced Design System 2008 Update 2, CDMA2K_CRC_Coder module documentation (courtesy of the Internet Archive)
  • III Full description
• Created: 14 October 2013
• Updated: 28 July 2023

CRC-12/DECT

width=12 poly=0x80f init=0x000 refin=false refout=false xorout=0x000 check=0xf5b residue=0x000 name="CRC-12/DECT"

• Class: academic
• Alias: X-CRC-12
• ETSI EN 300 175-3 version 2.5.1 (August 2013)
  • I Definition: Residue; full mathematical description (Section 6.2.5.4, pp.99–101)
• Created: 29 July 2010
• Updated: 15 February 2017

CRC-12/GSM

width=12 poly=0xd31 init=0x000 refin=false refout=false xorout=0xfff check=0xb34 residue=0x178 name="CRC-12/GSM"

• Class: academic
• ETSI TS 100 909 version 8.9.0 (January 2005)
  • I Full mathematical description (Section 5.1.5.1.4, p.72 — Section 5.1.6.1.4, p.75 — Section 5.1.7.1.4, p.77 — Section 5.1.8.1.4, p.78 — Section 5.1.9.1.4, p.81 — Section 5.1.10.1.4, p.85 — Section 5.1.11.1.4, p.87 — Section 5.1.12.1.4, p.91 — Section 5.1.13.1.4, p.93)
• Created: 17 February 2017

CRC-12/UMTS

width=12 poly=0x80f init=0x000 refin=false refout=true xorout=0x000 check=0xdaf residue=0x000 name="CRC-12/UMTS"

• Class: academic
• Alias: CRC-12/3GPP
• The crossed-endian definition is unusual but explicit. Researched by "markw_be" at the Computer Interfacing Forum.
• 3rd Generation Partnership Project (3GPP) TS 25.212 version 17.0.0 (March 2022) (zipped MS Word document) — ETSI TS 125 212 version 17.0.0 (May 2025)
  • I Mathematical description, defining Width, Poly, Init, Residue (Section 4.2.1.1, pp.19–20)
  • I Attachment relation, defining RefIn ^ RefOut (Section 4.2.1.2, p.20)
• Created: 10 December 2009
• Updated: 5 August 2023

CRC-13/BBC

width=13 poly=0x1cf5 init=0x0000 refin=false refout=false xorout=0x0000 check=0x04fa residue=0x0000 name="CRC-13/BBC"

• Class: attested
• S. R. Ely, D. T. Wright, British Broadcasting Corporation (March 1982), L.F. Radio-data: specification of the BBC experimental transmissions 1982
  • I Full mathematical description (Section 5.3, pp.4–5)
  • I Definition of bit order (Section 5.2, p.4)
  • I Worked example (as generator matrix) (Figure 10, p.10)
  • IV 1 additional codeword (Appendix, p.10)
    • 17777777​77776272​2 (octal)
• Created: 14 October 2013
• Updated: 6 February 2017

CRC-14/DARC

width=14 poly=0x0805 init=0x0000 refin=true refout=true xorout=0x0000 check=0x082d residue=0x0000 name="CRC-14/DARC"

• Class: attested
• The single codeword is supported by the codewords confirming CRC-6/DARC, defined identically apart from Poly in the same standard. The source presents the codeword in transmission order, whereas the codeword is composed of the bytes of data sent LSB first. The CRC mask is …FF 3F.
• ETSI EN 300 751 version 1.2.1 (January 2003)
  • I Definition: Width, Poly (Section 11.1, p.67)
  • I Definition: RefIn, RefOut (Section 12, pp.69–70)
  • IV 1 codeword (Section 11.1, p.67)
    • 02000102​37205052​4F4A4543​54204D41​494E4D45​4E553B08 (source: 40008040​EC040A4A​F252A2C2​2A04B282​9272B2A2​72AADC10)
  • See section 12 for details of the transmission order.
• Created: 14 December 2009
• Updated: 20 November 2018

CRC-14/GSM

width=14 poly=0x202d init=0x0000 refin=false refout=false xorout=0x3fff check=0x30ae residue=0x031e name="CRC-14/GSM"

• Class: academic
• ETSI TS 100 909 version 8.9.0 (January 2005)
  • I Full mathematical description (Section 3.9.1.2, p.28 — Section 3.9.5.2, p.40 — Section 3.10.1.2, p.42 — Section 3.10.9.2, p.54)
• Created: 17 February 2017

CRC-15/CAN

width=15 poly=0x4599 init=0x0000 refin=false refout=false xorout=0x0000 check=0x059e residue=0x0000 name="CRC-15/CAN"

• Class: academic
• Alias: CRC-15
• Robert Bosch GmbH (September 1991), CAN 2.0 Specification (courtesy of GitHub)
  • I Full definition (except Check) (Section 3.1.1, pp.13–14)
  • I Pseudocode
• Created: 2 November 2007
• Updated: 7 May 2022

CRC-15/MPT1327

width=15 poly=0x6815 init=0x0000 refin=false refout=false xorout=0x0001 check=0x2566 residue=0x6815 name="CRC-15/MPT1327"

• Class: attested
• MX-COM reference from Koopman and Chakravarty (2004).
• UK Radiocommunications Agency (20 June 1997), MPT 1327: A signalling standard for trunked private land mobile radio systems, 3rd edition (courtesy of UK National Archives)
  • I Full mathematical description (Section 3.2.3, p.3-3)
  • I Error control properties (Appendix 2, p.A2-1)
  • IV 1 codeword (Section 5.1.1, p.5-3; Appendix 3, p.A3-1)
    • 10101010​10101010​11000100​11010100​00000000​00000000​00000000​00000001​01010101​01010101​10001001​101011
• "whiteox11" (28 December 2011), "mpt1327 decoding" (video, embedded content; courtesy of YouTube)
  • II Transcript confirming implementation with 25 codewords (selection)
    • 10011111​11010010​10110100​11110011​11111011​01000100​01001111​0010110
    • 10101001​11000101​01100000​10100000​11011100​01101100​11101011​1011101
    • 10011111​11010001​01001010​01110010​01101001​01011000​10010010​1110000
    • 10011010​01000111​11000100​01101000​00001010​10101010​10111111​0011100
    • 10101011​10010110​10110100​00110010​01011110​10100000​11000010​0000100
• "radiowavemaniac" (21 November 2012), "RTL-SDR Trunkview Decoder MPT1327" (video)
  • II Transcript confirming implementation with 10 codewords
    • 10001010​00001100​00001100​01110010​00001000​01111000​11111100​0110000
    • 10001110​00001100​00001100​01110000​00010000​00000000​00001101​0100110
    • 10010011​01110000​11010100​01000011​11111111​10010000​00101110​1110100
    • 10010011​01100111​10011100​01000011​11111111​10010000​01100110​0110101
    • 10010011​01100111​10011100​11010010​01100001​01111100​01010000​1100011
    • 10010011​11111111​11100100​01011101​10011110​01111000​10101111​1101011
    • 10010011​00001011​11100100​00100101​10011110​01110000​11100100​0011011
    • 10010011​00001011​11100100​00100001​10011110​01100000​00100011​0011011
    • 10010011​01100110​10100100​01000011​11111111​10010000​01101111​1000111
    • 10010011​01100110​10110100​01000011​11111111​10010000​10111111​0001110
• MX-COM, Inc. (17 August 1998), Error detection and correction of MPT1327 formatted messages using MX429A or MX809 devices (courtesy of the Internet Archive)
  • III Full mathematical description (Section 1.2.1, p.1)
  • III Worked example (Section 1.2.2, p.2)
  • III Code: C (Section 1.2.3, p.3)
• reveng -m CRC-15/MPT1327 -t -X -c 9FD2B4F3​FB44 → 4F2C
• Unique effective solution of codeword set
• Created: 16 July 2012
• Updated: 2 August 2023

Disclaimer

Every effort has been made to ensure accuracy, however there may be occasional errors or omissions. All trademarks and registered trademarks are the intellectual property of their respective owners. The code and documentation included in this document are supplied without warranty, not even the implied warranties of merchantability or fitness for a particular purpose. In no event shall the author or his suppliers be liable for any loss, damage, injury or death, of any nature and howsoever caused, arising from the use of, or failure, inability or unwillingness to use, this software or documentation.

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Greg Cook,
https://reveng.sourceforge.io/crc-catalogue/1-15.htm Last updated 29 August 2024
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