List Decoding of Reed-Muller Codes Based on a Generalized Plotkin Construction


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.7   pp.1662-1666
Publication Date: 2013/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.1662
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Coding Theory
Reed-Muller code,  list decoding,  Plotkin construction,  

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Gopalan, Klivans, and Zuckerman proposed a list-decoding algorithm for Reed-Muller codes. Their algorithm works up to a given list-decoding radius. Dumer, Kabatiansky, and Tavernier improved the complexity of the algorithm for binary Reed-Muller codes by using the well-known Plotkin construction. In this study, we propose a list-decoding algorithm for non-binary Reed-Muller codes as a generalization of Dumer et al.'s algorithm. Our algorithm is based on a generalized Plotkin construction, and is more suitable for parallel computation than the algorithm of Gopalan et al. Since the list-decoding algorithms of Gopalan et al., Dumer et al., and ours can be applied to more general codes than Reed-Muller codes, we give a condition for codes under which these list-decoding algorithms works.