List Decoding of Reed-Solomon Codes from a Groebner Basis Perspective

Details List Decoding of Reed-Solomon Codes from a Groebner Basis Perspective List Decoding of Reed-Solomon Codes from a Groebner Basis Perspective

2006-01-02

arxiv.org/abs/math/0601022v3

Mathematics

Commutative Algebra

submitted to the Journal of Symbolic Computation; Shortened and revised version

Scientific paper

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.

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