On Representations of Algebraic-Geometric Codes for List Decoding

Authors:
Venkatesan Guruswami;Madhu Sudan
Affiliations:
-;-
Venue:
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Year:
2000

Citing 7
Cited 0

Decoding of Reed Solomon codes beyond the error-correction bound

Journal of Complexity
List decoding algorithms for certain concatenated codes

STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Decoding Hermitian Codes with Sudan's Algorithm

AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Improved Decoding of Reed-Solomon and Algebraic-Geometric Codes

FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Algebraic function fields over finite fields with many rational places

IEEE Transactions on Information Theory - Part 1
List decoding of algebraic-geometric codes

IEEE Transactions on Information Theory
A Hensel lifting to replace factorization in list-decoding of algebraic-geometric and Reed-Solomon codes

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show that all algebraic-geometric codes possess a succinct representation that allows for the list decoding algorithms of [15,7] to run in polynomial time. We do this by presenting a root-finding algorithm for univariate polynomials over function fields when their coefficients lie in finite-dimensional linear spaces, and proving that there is a polynomial size representation given which the root finding algorithm runs in polynomial time.