A Root-finding algorithm for list decoding of Reed-Muller codes

Title: A Root-finding algorithm for list decoding of Reed-Muller codes
Creator: Wu, Xinwen; Kuijper, Margreta; Udaya, Parampalli
Date: 2006
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/62625
Identifier: vital:3022
Identifier: https://doi.org/10.1109/TIT.2004.842765
Identifier: ISSN:0018-9448
Abstract: Let Fq[X1,...,Xm] denote the set of polynomials over Fq in m variables, and Fq[X1,...,Xm]≤u denote the subset that consists of the polynomials of total degree at most u. Let H(T) be a nontrivial polynomial in T with coefficients in Fq[X1,...,Xm]. A crucial step in interpolation-based list decoding of q-ary Reed-Muller (RM) codes is finding the roots of H(T) in Fq[X1,...,Xm]≤u. In this correspondence, we present an efficient root-finding algorithm, which finds all the roots of H(T) in Fq[X1,...,Xm]≤u. The algorithm can be used to speed up the list decoding of RM codes.; C1
Publisher: California, USA IEEE Institute of Electrical and Electronics Engineers
Relation: IEEE transactions on information theory Vol. 51, no. 3 (2006), p. 1190-1196
Rights: Copyright IEEE Institute of Electrical and Electronics Engineers Inc
Rights: This metadata is freely available under a CCO license
Subject: 0801 Artificial Intelligence and Image Processing; 1702 Cognitive Science; 0906 Electrical and Electronic Engineering
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