Book ChapterDOI
Decoding Hermitian Codes with Sudan's Algorithm
T. Hoholdt,R. Refslund Nielsen +1 more
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An efficient implementation of Sudan's algorithm for list decoding Hermitian codes beyond half the minimum distance is presented and a reduction of the problemof factoring the Q-polynomial to the problem of factoring a univariate polynomial over a large finite field is reduced.Abstract:
We present an efficient implementation of Sudan's algorithm for list decoding Hermitian codes beyond half the minimum distance. The main ingredients are an explicit method to calculate so-called increasing zero bases, an efficient interpolation algorithm for finding the Q- polynomial, and a reduction of the problemof factoring the Q-polynomial to the problem of factoring a univariate polynomial over a large finite field.read more
Citations
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Journal ArticleDOI
Improved decoding of Reed-Solomon and algebraic-geometry codes
Venkatesan Guruswami,Madhu Sudan +1 more
TL;DR: An improved list decoding algorithm for decoding Reed-Solomon codes and alternant codes and algebraic-geometry codes is presented and a solution to a weighted curve-fitting problem is presented, which may be of use in soft-decision decoding algorithms for Reed- Solomon codes.
Book
List Decoding of Error-Correcting Codes
Venkatesan Guruswami,Madhu Sudan +1 more
TL;DR: This thesis presents a detailed investigation of list decoding, and proves its potential, feasibility, and importance as a combinatorial and algorithmic concept and presents the first polynomial time algorithm to decode Reed-Solomon codes beyond d/2 errors for every value of the rate.
Journal ArticleDOI
List decoding of q-ary Reed-Muller codes
Ruud Pellikaan,Xin-Wen Wu +1 more
TL;DR: This correspondence shows that q-ary RM codes are subfield subcodes of RS codes over F/sub q//sup m/ and presents a list-decoding algorithm, applicable to codes of any rates, and achieves an error-correction bound n(1-/spl radic)/n.
Journal ArticleDOI
Efficient root-finding algorithm with application to list decoding of algebraic-geometric codes
Xin-Wen Wu,Paul H. Siegel +1 more
TL;DR: A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance t from the received vector, where t can be greater than the error-correction bound, and an efficient list-decoding algorithm for algebraic-geometric codes is given.
Proceedings ArticleDOI
A displacement approach to efficient decoding of algebraic-geometric codes
Vadim Olshevsky,Amin Shokrollahi +1 more
TL;DR: A unified framework for derivation of efficient list decoding algorithms for algebraicgeometric codes is developed using methods originating in numerical analysis and appropriate displacement operators for matrices that occur in the context of list decoding are derived.
References
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Book
Algebraic Function Fields and Codes
TL;DR: This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded and contains numerous exercises that help the reader to understand the basic material.
Journal ArticleDOI
Improved decoding of Reed-Solomon and algebraic-geometry codes
Venkatesan Guruswami,Madhu Sudan +1 more
TL;DR: An improved list decoding algorithm for decoding Reed-Solomon codes and alternant codes and algebraic-geometry codes is presented and a solution to a weighted curve-fitting problem is presented, which may be of use in soft-decision decoding algorithms for Reed- Solomon codes.
Journal ArticleDOI
Decoding of Reed Solomon Codes beyond the Error-Correction Bound
TL;DR: To the best of the knowledge, this is the first efficient (i.e., polynomial time bounded) algorithm which provides error recovery capability beyond the error-correction bound of a code for any efficient code.