# CRC Polynomial Selection

Philip Koopman, Carnegie Mellon University

## Good HD=5 Polynomials

Selection rules:

• Pick an optimal HD=5 length.

Note that alternate HD=5 choices can be found via the secondary property criteria for HD=3 and HD=4 polynomials.

 CRC  Bits HD=5  Length (Bits) Secondary  Property Polynomial Nickname HD  Lengths 7 4 none (0x72; 0xe5) FT2; CRC-7-MVB; CRC-7F/5 ("345p") (*p) {120,7,4} 8 9 none (0xeb; 0x1d7) CRC-8F/5 {9,9,9,2,1} 9 13 none (0x185; 0x30b) CRC-9F/5 ("1413") {96,16,13} 10 21 none (0x2b9; 0x573) CRC-10F/5 {21,21,21,3,3} 11 26 none (0x5d7; 0xbaf) CRC-11F/5 (*p) {2036,28,26,3,2,2,1} 12 53 HD=6@ 10 (0xbae; 0x175d) CRC-12F/5 {53,53,53,10,2,2,2} 13 52 HD=6@ 52 (0x1e97; 0x3d2f) CRC-13F/6.2 (*o) {52,52,52,52,4,4,1,1} 14 113 HD=6@ 21 (0x212d; 0x425b) CRC-14K/5 {113,113,113,21,3} 15 136 HD=6@ 16 (0x6a8d; 0xd51b) CRC-15F/5 {136,136,136,16,5,2,2} 16 241 HD=6@ 35 (0xac9a; 0x15935) C3; CRC-16F/5 {241,241,241,35,10,8,3} 17 240 HD=6@ 240 (0x1724e; 0x2e49d) CRC-17K/6 (*o) {240,240,240,240,11,11,3,3} 18 493 HD=6@ 61 (0x39553; 0x72aa7) CRC-18K/5 {493,493,493,61,4,4,3,3,2} 19 494 HD=6@ 494 (0x5685a; 0xad0b5) CRC-19K/6 (*o) {494,494,494,494,16,16,2,2} 20 1005 HD=6@ 105 (0xc8a89; 0x191513) CRC-20K/5 {1005,1005,1005,105,28,10,4} 21 1004 HD=6@ 1004 (0x1edfb7; 0x3dbf6f) CRC-21K/6 (*o) {1004,1004,1004,1004,28,28,7,7,1,1,1,1,1,1,1,1} 22 2025 HD=6@ 158 (0x2a952a; 0x552a55) CRC-22K/5 {2025,2025,2025,158,2,2,2,2,2} 23 2026 HD=6@ 2026 (0x6bc0f5; 0xd781eb) CRC-23K/6 (*o) {2026,2026,2026,2026,39,39,11,11,2,2,1,1} 24 4073 HD=6@ 228 (0x98ff8c; 0x131ff19) CRC-24/5.1 {4073,4073,4073,228,13,9,9,9,1,1,1,1,1} 25 4072 HD=6 @ 4072 (0x1b9189d; 0x372313b) CRC-25K/6 (*o) {4072,4072,4072,4072,65,65,7,7,7,7,4,4} 26 8165 HD=6@ 328 (0x2c45446; 0x588a88d) CRC-26K/5 {8165,8165,8165,328,89,32,13,13,7} 27 8166 HD=6@8166 (0x6c3ff0d; 0xd87fe1b) CRC-27K/6 (*o) {8166,8166,8166,8166,86,86,16,16,1,1,1,1,1,1,1,1} 28 16357 HD=6@488 (0x9037604; 0x1206ec09) CRC-28K/5 {16357,16357,16357,488,35,35,8,8,3} 29 16356 HD=6@ 16356 (0x1cf492f3; 0x39e925e7) CRC-29K/6 (*o) {16356,16356,16356,16356,66,66,26,26,12,12,3,3,3,3,1,1} 30 32737 HD=6@ 514 (0x2adf3aaf; 0x55be755f) CRC-30K/5 {32737,32737,32737,514,237,74,23,23,16,5,2,2,2,2,2,2,2,2,1} 31 32738 HD=6@ 32738 0(0x74f9e7cb; 0xe9f3cf97) CRC-31K/6 (*o) {32738,32738,32738,32738,151,151,14,14,13,13,7,7,1,1,1,1,1,1,1,1} 32 65505 HD=6@ 1060 (0xd419cc15; 0x1a833982b) CRC-32/5.1 (**) {65505,65505,65505,1060,81,58,27,27,21,17,3,3,3}

Note: minimum dataword length evaluated is 4 bits. Yellow highlighted cells indicated work in progress/missing data.

See the NOTES PAGE for interpreting this data. Last update 1/2019.