CRC Polynomial Selection

Philip Koopman, Carnegie Mellon University

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Good HD=4 Polynomials

Selection rules:

  1. Pick an optimal HD=4 length.
  1. Pick longest secondary property length available for that HD=4 length

Note that all primitive polynomials times (x+1) annoted as (*op) have HD=4 up to length ((2**(k-1))-CrcSize-1). HD=3 secondary property was not selected because all such polynomials have the same length for HD=3 as for HD=4.

 CRC 
Bits
 HD=4 
Length
(Bits)
 Secondary 
Property
 Polynomial   Nickname  HD
 Lengths 
5 10 none (0x15; 0x2b) CRC-5; CRC-5-ITU;
CRC-5F/4 (*op)
{10,10}
6 25 none (0x23; 0x47) CRC-6-CDMA2000-B (*op) {25,25}
7 56 none (0x5b; 0xb7) CRC-7F/4.2 (*op) {56,56,2,2}
8 119 none (0x83; 0x107) ATM-8; CRC-8P (*op) {119,119}
9 246 HD=5,6@ 5 (0x17d; 0x2fb) CRC-9F/4.2 (*op) {246,246,5,5,1,1}
10 501 HD=5,6@ 10 (0x247; 0x48f) CRC-10F/4.2 (*op) {501,501,10,10}
11 1012 HD=5,6@ 17 (0x583; 0xb07) CRC-11F/4.2 (*op) {1012,1012,17,17}
12 2035 HD=5,6@ 25 (0x8f3; 0x11e7) CRC-12F/4.2 (*op) {2035,2035,25,25,1,1}
13 4082 HD=5,6@ 32 (0x12e6; 0x25cd) CRC-13F/4.2 (*op) {4082,4082,32,32,4,4}
14 8177 HD=5,6@ 57 (0x2322; 0x4645) CRC-14K/4.2 (*op) {8177,8177,57,57}
15 16368 HD=5,6@ 68 (0x4306; 0x860d) CRC-15F/4.2 (*op) {16368,16368,68,68}
16 32751 HD=5,6@ 93 (0xd175; 0x1a2eb) C5; CRC-16F/4.2 (*op) {32751,32751,93,93,11,11,2,2}
17 65518 HD=5,6@ 118 (0x1165d; 0x22cbb) CRC-17K/4 (*op) {65518,65518,118,118,10,10,3,3}
18 131053 HD=5,6@ 167 (0x25f53; 0x4bea7) CRC-18K/4 (*op) {131053,131053,167,167,10,10,5,5,2,2}
19 262124 HD=5,6@ 206 (0x77b0f; 0xef61f) CRC-19K/4 (*op) {262124,262124,206,206,15,15,1,1,1,1,1,1}
20 524267 HD=5,6@ 294 (0xc1acf; 0x18359f) CRC-20K/4 (*op) {524267,524267,294,294,24,24,3,3,1,1}
21 1048554 HD=5,6@ 370 (0x10df8f; 0x21bf1f) CRC-21K/4 (*op) {1048554,1048554,370,370,26,26,1,1,1,1,1,1}
22 2097129 HD=5,6@ 509 (0x248794; 0x490f29) CRC-22K/4 (*op) {2097129,2097129,509,509,26,26,12,12}
23 4194280 HD=5,6@ 601 (0x400154; 0x8002a9) CRC-23K/4 (*op) {4194280,4194280,601,601}
24 8388583 HD=5,6@ 822 (0x9945b1; 0x1328b63) CRC-24/4 (*op) {8388583,8388583,822,822,37,37,12,12,6,6}
25 16777190 HD=5,6@ 1059 (0x10bba2d; 0x217745b) CRC-25K/4 (*op) 16777190,16777190,1059,1059,38,38,8,8,6,6,2,2}
26 33554405 HD=5,6@ 1493 (0x278b495; 0x4f1692b) CRC-26K/4 (*op) {33554405,33554405,1493,1493,24,24,18,18,9,9,4,4}
27 67108836 HD=5,6@ 1785 (0x745e8bf; 0xe8bd17f) CRC-27K/4 (*op) {67108836,67108836,1785,1785,45,45,10,10,6,6,2,2,1,1,1,1}
28 134217699 HD=5,6@ 2311 (0xb67b511; 0x16cf6a23) CRC-28K/4 (*op) {134217699,134217699,2311,2311,92,92,24,24,8,8,4,4,2,2}
29 268435426 HD=5,6@ 2859 (0x11c4dfb5; 0x2389bf6b) CRC-29K/4 (*op) {268435426,268435426,2859,2859,116,116,30,30,6,6,6,6,4,4,1,1}
30 536870881 HD=5,6@ 3769 (0x2254329d; 0x44a8653b) CRC-30K/4 (*op) {536870881,536870881,3769,3769,99,99,44,44,10,10,6,6}
31 1073741792 HD=5,6@ 4957 (0x52aa4332; 0xa5548665) CRC-31K/4 (*op) {1073741792,1073741792,4957,4957,157,157,35,35,9,9,3,3}
32  2147483615  HD=5,6@ 6167 (0xc9d204f5; 0x193a409eb) CRC-32K/4.2 (*op) {2147483615,2147483615,6167,6167,148,148,44,44,25,25,8,8,3,3}

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 July 19, 2015.

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This work is copyright 2015 by Philip Koopman. Licensed under a Creative Commons Attribution 4.0 International License.