BCH and Hamming Codes
BCH codes for blocklength of up to 1023 and different error correction capability t can be downloaded. Note, that Hamming codes are BCH codes with t=1. BCH and Hamming codes are cyclic codes, that can be described by a parity check matrix, where each row is a shifted version of the neighboring rows (We have called this form "strip format", because the '1's form diagonal stips in the matrix).
| N | K | Rate | t | Parity Check Matrix |
|---|---|---|---|---|
| 7 | 4 | 0.57 | 1 | matrix or alist |
| 15 | 11 | 0.73 | 1 | matrix or alist |
| 15 | 7 | 0.47 | 2 | matrix or alist |
| 31 | 26 | 0.84 | 1 | matrix or alist |
| 31 | 21 | 0.68 | 2 | matrix or alist |
| 31 | 16 | 0.52 | 3 | matrix or alist |
| 31 | 11 | 0.35 | 5 | matrix or alist |
| 63 | 57 | 0.90 | 1 | matrix or alist |
| 63 | 51 | 0.81 | 2 | matrix or alist or 1-min |
| 63 | 45 | 0.71 | 3 | matrix or alist or 1-min |
| 63 | 39 | 0.62 | 4 | matrix or alist or 1-min |
| 63 | 36 | 0.57 | 5 | matrix or alist or 1-min |
| 63 | 30 | 0.48 | 6 | matrix or alist or 1-min |
| 127 | 120 | 0.94 | 1 | matrix or alist |
| 127 | 113 | 0.89 | 2 | matrix or alist |
| 127 | 106 | 0.83 | 3 | matrix or alist |
| 127 | 99 | 0.78 | 4 | matrix or alist or 1-min |
| 127 | 92 | 0.72 | 5 | matrix or alist or 1-min |
| 127 | 85 | 0.67 | 6 | matrix or alist or 1-min |
| 127 | 78 | 0.61 | 7 | matrix or alist or 1-min |
| 127 | 71 | 0.56 | 9 | matrix or alist or 1-min |
| 127 | 64 | 0.50 | 10 | matrix or alist or 1-min |
| 255 | 247 | 0.97 | 1 | matrix or alist |
| 255 | 239 | 0.94 | 2 | matrix or alist or 1-min |
| 255 | 231 | 0.91 | 3 | matrix or alist |
| 255 | 223 | 0.87 | 4 | matrix or alist |
| 255 | 215 | 0.84 | 5 | matrix or alist |
| 255 | 207 | 0.81 | 6 | matrix or alist or 1-min |
| 255 | 199 | 0.78 | 7 | matrix or alist |
| 255 | 191 | 0.75 | 8 | matrix or alist |
| 255 | 163 | 0.64 | 12 | matrix or alist or 1-min |
| 511 | 502 | 0.98 | 1 | matrix or alist |
| 511 | 493 | 0.96 | 2 | matrix or alist |
| 511 | 484 | 0.95 | 3 | matrix or alist |
| 511 | 475 | 0.93 | 4 | matrix or alist |
| 511 | 466 | 0.91 | 5 | matrix or alist |
| 511 | 457 | 0.89 | 6 | matrix or alist |
| 1023 | 1013 | 0.99 | 1 | matrix or alist |
| 1023 | 1003 | 0.98 | 2 | matrix or alist |
| 1023 | 993 | 0.97 | 3 | matrix or alist |
| 1023 | 983 | 0.96 | 4 | matrix or alist |
DVB S-2 BCH Codes
DVB S-2 uses BCH codes as an outer code (in addition to the inner LDPC). Matrices for the short frame are provided.
Extended BCH Codes
Extended BCH codes have an additional parity bit, that checks all bit positions.