On the Number of Minimum Weight Codewords of Subcodes of Reed-Muller Codes

Hitoshi TOKUSHIGE, Toyoo TAKATA, Tadao KASAMI

Summary :

In this paper, we consider linear subcodes of RM_r,m whose bases are formed from the monomial basis of RM_r,m by deleting ΔK monomials of degree r where ΔK < . For such subcodes, a procedure for computing the number of minimum weight codewords is presented and it is shown how to delete ΔK monomials in order to obtain a subcode with the smallest number of codewords of the minimum weight. For ΔK 3, a formula for the number of codewords of the minimum weight is presented. A (64,40) subcode of RM_3,6 is being considered as an inner code in a concatenated coding system for NASA's high-speed satellite communications. For (64,40) subcodes, there are three equivalent classes. For each class, the number of minimum weight codewords, that of the second smallest weight codewords and simulation results on error probabilities of soft-decision maximum likelihood decoding are presented.

• Publication: IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.10 pp.1990-1997
• Publication Date: 1998/10/25
• Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
• Category: Coding Theory

Authors

Hitoshi TOKUSHIGE
Toyoo TAKATA
Tadao KASAMI

Keyword

minimum weight codeword,  Reed-Muller code,  subcode