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 A: Binary Primitive Polynomials
Appendix A presents a list of binary primitive polynomials p( x) = x m + p m ?1 x m ?1 + p m ?2 x m ?2 + ... + p 1 x + p 0 of degree m, where p j = 0 and 1, 0 ? j ? m ? 1, and 2 ? m ? 7.
| m | p(x) |
|---|---|
| 2 | x 2 + x + 1 |
| 3 | x 3 + x + 1 |
| 3 | x 3 + x 2 + 1 |
| 4 | x 4 + x + 1 |
| 4 | x 4 + x 3 + 1 |
| 5 | x 5 + x 2 + 1 |
| 5 | x 5 + x 3 + 1 |
| 5 | x 5 + x 3 + x 2 + x + 1 |
| 5 | x 5 + x 4 + x 2 + x + 1 |
| 5 | x 5 + x 4 + x 3 + x + 1 |
| 5 | x 5 + x 4 + x 3 + x 2 + 1 |
| 6 | x 6 + x + 1 |
| 6 | x 6 + x 4 + x 3 |
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