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

Kwankyu Lee; Michael E. O'Sullivan

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

Kwankyu Lee·Michael E. O'Sullivan

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Abstract

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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BibTeX RIS

Kwankyu Lee, Michael E. O'Sullivan. 2007-12-11. List Decoding of Reed-Solomon Codes from a Groebner Basis Perspective. https://arxiv.org/abs/math/0601022

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