A lower bound on the optimum distance profiles of the second-order Reed-Muller codes

Authors:
Yanling Chen;A. J. Han Vinck
Affiliations:
Fraunhofer lESE, Kaiserslautern, Germany;Institute for Experimental Mathematics, University of Duisburg-Essen, Essen, Germany
Venue:
IEEE Transactions on Information Theory
Year:
2010

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ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3

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Abstract

In this paper, we give a lower bound for the optimum distance profiles of the second-order Reed-Muller code in the dictionary order and in the inverse dictionary order. In particular, we investigate the second-order Reed-Muller codes of length ≤256. We show that the bound is tight in both orders for the codes of length ≤128.