On computing the performance probabilities of Reed-Solomon codes

Abstract

The performance of linear block codes used for pure error correction, pure error detection or a combination of the two has been a subject of much study ([3]-[5], [7]-[9]). In particular it is desirable to determine the probability of undetected error when a code is used for forward error correction. In this note, we derive an effective algorithm for assessing the performance of an (N,k) Reed-Solomon code over GF(q), where N is the number of symbols in the codeword, k the number of information symbols and N=q-l. A Reed-Solomon code is an example of a special class of codes called maximum distance separable. These codes are characterlsed by the property that the minimum distance d=N-k+l. Furthermore, the weight distribution of an [N,k,d=N-k+l] mds code over GF(q) is completely determined by its parameters thus ([I] p429 or [6] p321):