List Decoding of Reed-Solomon Codes from a Groebner Basis Perspective
交换代数
2007-12-11 v3 组合数学
摘要
The interpolation step of Guruswami and Sudan's list decoding of Reed-Solomon codes poses the problem of finding the minimal polynomial of an ideal with respect to a certain monomial order. An efficient algorithm that solves the problem is presented based on the theory of Groebner bases of modules. In a special case, this algorithm reduces to a simple Berlekamp-Massey-like decoding algorithm.
引用
@article{arxiv.math/0601022,
title = {List Decoding of Reed-Solomon Codes from a Groebner Basis Perspective},
author = {Kwankyu Lee and Michael E. O'Sullivan},
journal= {arXiv preprint arXiv:math/0601022},
year = {2007}
}
备注
submitted to the Journal of Symbolic Computation; Shortened and revised version