USNA Mathematics Department seminar

Title:

Abstract: The theory of error correcting codes, with applications ranging from satellite communications to compact discs, stands as one of the success stories of applied modern algebra. "Burst" correcting codes are ones designed for use in situations where errors tend to cluster near one another.

Binary quasi-cyclic (m(2^m - 1), m(2^m- 3)) codes derived from (n, n - 3) Reed-Solomon (R-S) codes are presented that correct all burst errors of length at most m + 1. Their burst correction capability is similar to that achieved by binary versions of (n, n-4) R-S codes, yet, for the same length, they require m fewer check digits. The burst error decoding algorithms that are given are elementary and may be implemented on either the GF(2^m) or binary level. Used for detection purposes only, these codes can detect all burst errors of length 3m.