List decoding of Reed-Solomon codes from a Gröbner basis perspective

Authors:
Kwankyu Lee;Michael E. OSullivan
Affiliations:
School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Republic of Korea;Department of Mathematics and Statistics, San Diego State University, San Diego, USA
Venue:
Journal of Symbolic Computation
Year:
2008

Citing 4
Cited 4

Decoding of Reed Solomon codes beyond the error-correction bound

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Improved decoding of Reed-Solomon and algebraic-geometry codes

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Linear diophantine equations over polynomials and soft decoding of Reed-Solomon codes

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On the key equation

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List decoding of Hermitian codes using Gröbner bases

Journal of Symbolic Computation
Key equations for list decoding of Reed-Solomon codes and how to solve them

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Algebraic soft-decision decoding of Hermitian codes

IEEE Transactions on Information Theory
Efficient interpolation in the Guruswami-Sudan algorithm

IEEE Transactions on Information Theory

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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 Grobner bases of modules. In a special case, this algorithm reduces to a simple Berlekamp-Massey-like decoding algorithm.