This document describes a fully-specified simple Forward Error Correction (FEC) scheme for Reed-Solomon codes over the finite field (also known as the Galois Field) GF(2^^m), with 2 <= m <= 16, that can be used to protect arbitrary media streams along the lines defined by FECFRAME. The Reed-Solomon codes considered have attractive properties, since they offer optimal protection against packet e...

For a linear code, deep holes are defined to be vectors that are further away from codewords than all other vectors. The problem of deciding whether a received word is a deep hole for generalized ReedSolomon codes is proved to be co-NP-complete [9][5]. For the extended Reed-Solomon codes RSq(Fq, k), a conjecture was made to classify deep holes in [5]. Since then a lot of effort has been made to...

– The Welch-Berlekamp (WB) key equation arises in the decoding of Reed-Solomon (RS) codes over finite fields where the decoding problem is viewed as a rational interpolation problem. The significance of this decoding approach lies in the fact that it does not require the prior evaluation of power sum symmetric functions, i.e. the so-called syndrome vector corresponding to a received word. It ha...

| Concatenated codes have long been used as a practical means of combating errors on very noisy channels. In this paper we investigate the performance of concatenated systems that employ inner convolutional codes with outer Reed-Solomon codes. We determine upper and lower bounds of the optimal inner code rate for a selected overall code rate on a binary symmetric channel .

Self-dual maximum distance separable codes (self-dual MDS codes) and self-dual near (NMDS) are very important in coding theory practice. Thus, it is interesting to construct or NMDS codes. In this paper, we not only give parity-check matrices of dual twisted generalized Reed–Solomon (TGRS but also present a sufficient necessary condition TGRS over $${\mathbb {F}}_q$$ with q an odd prime. Moreov...

It is shown that good linear [n, k, d] codes over a finite field GF(q) can be constructed by concatenating the generator matrices of Reed-Solomon codes. For the first interesting case of k = 3, it is shown that many of the codes obtained via projective geometry techniques can readily be obtained via the proposed algebraic approach.

Given an error-correcting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding Reed-Solomon codes. The list decoding problem for Reed-Solomon codes reduces to the following “curve-fitting” probl...