List decoding of Reed-Solomon codes from a Gröbner basis perspective
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Publication:931140
DOI10.1016/j.jsc.2008.01.002zbMath1214.94080arXivmath/0601022OpenAlexW2022879455MaRDI QIDQ931140
Michael E. O'Sullivan, Kwankyu Lee
Publication date: 25 June 2008
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0601022
Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Decoding (94B35)
Related Items (11)
Computing minimal interpolation bases ⋮ List decoding of repeated codes ⋮ Minimal Gröbner bases and the predictable leading monomial property ⋮ Multi-trial Guruswami-Sudan decoding for generalised Reed-Solomon codes ⋮ Generic interpolation polynomial for list decoding ⋮ List decoding algorithm based on voting in Gröbner bases for general one-point AG codes ⋮ Row reduction applied to decoding of rank-metric and subspace codes ⋮ An iterative algorithm for parametrization of shortest length linear shift registers over finite chain rings ⋮ Key equations for list decoding of Reed-Solomon codes and how to solve them ⋮ Power decoding Reed-Solomon codes up to the Johnson radius ⋮ List decoding of Hermitian codes using Gröbner bases
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- Linear Diophantine Equations Over Polynomials and Soft Decoding of Reed–Solomon Codes
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- Using Algebraic Geometry
- On the key equation
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