Error-Control Block Codes for Communications Engineers
An engineer s guide to the theory behind the common random-error-control block codes, and their applications in digital communications.
TABLE OF CONTENTS Error-Control Block Codes for Communications Engineers
Appendix D: Generator Polynomials of Binary, Narrow-Sense, Primitive BCH Codes
Appendix D presents a list of generator polynomials of binary, narrow-sense, primitive BCH codes of designed error-correcting power t d. Table D.1 lists the code dimension k, codeword length n, the designed Hamming distance ? d = 2 t d + 1, and the generator polynomial g( x) = x n ? k + g n ? k ?1 x n ? k ?1 + g n ? k ?2 x n ? k ?2 + ... + g 1 x + g 0 of the codes, where g j = 0 and 1, 0 ? j ? n ? k ? 1, and n = 7, 15, 31, 63, 127.
| n | k | Designed Distance 2 t d + 1 | g ( x) |
|---|---|---|---|
| 7 | 4 | 3 | x 3 + x + 1 |
| 15 | 11 | 3 | x 4 + x + 1 |
| 15 | 7 | 5 | x 8 + x 7 + x 6 + x 4 + 1 |
| 15 | 5 | 7 | x 10 + x 8 + x 5 + x 4 + x 2 + x + 1 |
| 31 | 26 | 3 | x 5 + x 2 + 1 |
| 31 | 21 | 5 | x 10 |
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