Fast Decoding of the p-Ary First-Order Reed-Muller Codes Based On Jacket Transform

Moon Ho LEE  Yuri L. BORISSOV  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.3   pp.901-904
Publication Date: 2008/03/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.3.901
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Coding Theory
p-ary first-order Reed-Muller codes,  decoding algorithms,  Jacket matrix,  

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We propose a fast decoding algorithm for the p-ary first-order Reed-Muller code guaranteeing correction of up to errors and having complexity proportional to nlog n, where n = pm is the code length and p is an odd prime. This algorithm is an extension in the complex domain of the fast Hadamard transform decoding algorithm applicable to the binary case.