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Catalogue of parametrised CRC algorithms with 15 or fewer bits

CRC-3/ROHC

width=3 poly=0x3 init=0x7 refin=true refout=true xorout=0x0 check=0x6 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

CRC-4/ITU

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

• Class: academic
• 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

CRC-5/EPC

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

• Class: attested
• Used in standardised RFID tags.
• EPCglobal Inc™ (23 October 2008), UHF Class 1 Gen 2: Air Interface Protocol Standard version 1.2.0
  • I Definition: Width, Poly, Init, Residue (Table 6.12, p.35)
  • I Definition: RefIn (Annex F, p.98)
  • I Shift register circuit diagram (Annex F, p.98)
• 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
  • IV 1 codeword
    • 10000001​00000000​010011
• Created: 20 May 2009
• Updated: 19 February 2012

CRC-5/ITU

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

• Class: academic
• ITU-T Recommendation G.704 (October 1998)
  • I 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: 1 July 2011

CRC-5/USB

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

• Class: third-party
• Anonymous (10 July 1997), "Cyclic Redundancy Checks in USB" (Draft) (courtesy of USB Implementers Forum, Inc.)
  • III Definition: Width, Poly, Init, XorOut (p.2)
  • III Code: Perl (pp.3–4)
  • IV 4 codewords (p.5)
    • 10101000​11110111
    • 01011100​10111100
    • 00001110​01001110
    • 10000000​00010111
• Created: 1 December 2007
• Updated: 29 January 2011

CRC-6/DARC

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

• Class: attested
• ETSI EN 300 751 version 1.2.1 (January 2003) (registration required)
  • 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 = 2923
    • 01010011​00011101 = CAB8
    • 00001100​01000000​00100000​00101101 = 300204B4
  • 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 1001010011 0101001100 00001100010000000010000000 → 20 B8 B4
• Unique effective solution of codeword set
• Created: 14 December 2009
• Updated: 1 June 2012

CRC-6/ITU

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

• Class: academic
• 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

CRC-7

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

• Class: academic
• Used in the MultiMediaCard interface.
• 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)
• Created: 7 October 2008
• Updated: 19 January 2012

CRC-7/ROHC

width=7 poly=0x4f init=0x7f refin=true refout=true xorout=0x00 check=0x53 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: 1 July 2011

CRC-8

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

• Class: confirmed
• 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 (courtesy of Rbytes Reviews)
  • II Implementation
• John Milios, USAR Systems, Inc. (13 April 1999), Firmware CRC-8 implementations for SMBus
  • III Definition: Width, Poly (pp.1–2)
  • III Worked examples (pp.2–7)
  • III Code: 6805 assembler (pp.5–16)
• Michael Niedermayer (7 January 2013), Libav 9.1 module libav-9.1/libavutil/crc.c
  • IV 1 codeword
    • 1999 bytes (i+i*i) plus E3
• Created: 30 March 2005
• Updated: 11 January 2013

CRC-8/DARC

width=8 poly=0x39 init=0x00 refin=true refout=true xorout=0x00 check=0x15 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) (registration required)
  • 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 = 80C0EB
  • See section 12 for details of the transmission order.
• Created: 14 December 2009
• Updated: 19 January 2011

CRC-8/EBU

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

• Class: attested
• 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

CRC-8/I-CODE

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

• Class: attested
• Philips Semiconductors (30 January 2004), SL2 ICS11 Product Specification (courtesy of NXP)
  • I Definition: Width, Poly, Init (Section 10.1, p.26)
  • I Code: C (Section 10.3.1, pp.27–29)
  • I Worked example (as code trace) (Section 10.3.1, p.29)
• Created: 3 November 2007
• Updated: 29 January 2011

CRC-8/ITU

width=8 poly=0x07 init=0x00 refin=false refout=false xorout=0x55 check=0xa1 name="CRC-8/ITU"

• Class: academic
• 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 (RTF)
  • I Full mathematical description (Section 2.2.6)
• Created: 19 April 2009
• Updated: 11 January 2013

CRC-8/MAXIM

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

• Class: attested
• Alias: 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 (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: 40000000​FBC52B24 where 40 = CRC
    • DS1920: A0000000​FBC52B10
    • DS1921G: 89000000​FBC52B21
    • DS1971: 54000000​FBC52B14
    • DS1971: D4000000​FBD8B314
    • DS1973: F3000000​FBC52B23
    • DS1973: 73000000​FBD8B323
    • DS1982: 97000000​FBC52B09
    • DS1982: 17000000​FBD8B309
    • DS1985: ED000000​FBC52B0B
    • DS1985: 6D000000​FBD8B30B
    • DS1986: 19000000​FBC52B0F
    • DS1986: 99000000​FBD8B30F
    • DS1995: D0000000​FBC52B0A
    • DS1996: 5E000000​FBC52B0C
• Created: 26 April 2009
• Updated: 14 January 2013

CRC-8/ROHC

width=8 poly=0x07 init=0xff refin=true refout=true xorout=0x00 check=0xd0 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: 1 July 2011

CRC-8/WCDMA

width=8 poly=0x9b init=0x00 refin=true refout=true xorout=0x00 check=0x25 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)
• 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)
• "V_MAX_V" (26 October 2009), Computer Interfacing Forum topic 1431
  • 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: 11 January 2013

CRC-10

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

• Class: attested
• 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
  • 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 6 additional codewords (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: 11 January 2013

CRC-11

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

• Class: attested
• FlexRay Consortium (October 2010), FlexRay Communications System Protocol Specification, version 3.0.1
  • 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
  • IV 1 codeword (Section 2.7.5, p.681)
    • 11 00000000010 0000001 00000100110, CRC = 026
• Robert Bosch GmbH (3 December 2007), E-Ray FlexRay IP Module, Application Note 2
  • IV 3 codewords (Section 4.4.3, pp.26–30; researched by Vivek Rajan)
    • 11 00000000001 0001000 00100011011, CRC = 11B
    • 11 00000000010 0001000 01100000100, CRC = 304
    • 00 00000000011 0001000 10111010010, CRC = 5D2
• Created: 3 November 2007
• Updated: 11 January 2013

CRC-12/3GPP

width=12 poly=0x80f init=0x000 refin=false refout=true xorout=0x000 check=0xdaf name="CRC-12/3GPP"

• Class: academic
• 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 11.4.0 (December 2012) (zipped MS Word document) — ETSI TS 125 212 version 11.3.0 (September 2012) (registration required)
  • I Mathematical description, defining Width, Poly, Init, Residue (Section 4.2.1.1, p.16)
  • I Attachment relation, defining RefIn ^ RefOut (Section 4.2.1.2, p.16)
• Created: 10 December 2009
• Updated: 13 January 2013

CRC-12/DECT

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

• Class: academic
• Alias: X-CRC-12
• ETSI EN 300 175-3 version 2.4.1 (April 2012) (registration required)
  • I Full mathematical description (Section 6.2.5.4, pp.96–8)
• Created: 29 July 2010
• Updated: 19 January 2012

CRC-14/DARC

width=14 poly=0x0805 init=0x0000 refin=true refout=true xorout=0x0000 check=0x082d 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 standard presents the codeword in transmission order, whereas the bytes of data are sent LSB first. The CRC mask is …FF 3F.
• ETSI EN 300 751 version 1.2.1 (January 2003) (registration required)
  • 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: 19 February 2012

CRC-15

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

• Class: academic
• Robert Bosch GmbH (September 1991), CAN 2.0 Specification
  • I Full definition (except Check) (Section 3.1.1, pp.13–14)
  • I Pseudocode
• Created: 2 November 2007
• Updated: 11 January 2013

CRC-15/MPT1327

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

• Class: attested
• MX-COM reference from Koopman (2004). Implementation confirmed by a transcript recorded by "whiteox11" (2011) with 25 unique codewords.
• UK Radiocommunications Agency (20 June 1997), MPT 1327: A signalling standard for trunked private land mobile radio systems, 3rd edition (courtesy of Ofcom)
  • 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
• MPT 1327 trunked radio networks
  • II Implementation
• MX-COM, Inc. (17 August 1998), Error detection and correction of MPT1327 formatted messages using MX429A or MX809 devices (courtesy of CML Microcircuits)
  • 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)
• Created: 16 July 2012
• Updated: 13 August 2012

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.

Greg Cook,
http://reveng.sourceforge.net/crc-catalogue/1-15.htm Last updated 16 January 2013
Links last verified 10 January 2013

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