On the Number of Minimum Weight Codewords of Subcodes of Reed-Muller Codes (Special Section on Information Theory and Its Applications)
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概要
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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 △K monomials of degree r where △K < (^m_r). For such subcodes, a procedure for computing the number of minimum weight codewords is presented and it is shown how to delete △K monomials in order to obtain a subcode with the smallest number of codewords of the minimum weight. For △K≦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.
- 社団法人電子情報通信学会の論文
- 1998-10-25
著者
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Kasami Tadao
Faculty of Graduate School of Information Science, Nara Institute of Science and Technology
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TOKUSHIGE Hitoshi
Graduate School of Information Science, Nara Institute of Science and Technology
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Tokushige H
Hiroshima City Univ. Hiroshima‐shi Japan
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Tokushige Hitoshi
Graduate School Of Information Science Nara Institute Of Science And Technology
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Kasami Tadao
Faculty Of Graduate School Of Information Science Nara Institute Of Science And Technology
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Takata Toyoo
Faculty Of Software And Information Science Iwate Prefectural University
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Takata Toyoo
Faculty Of Sortware And Information Science Iwate Prefectural University
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Kasami Tadao
Faculty Of Information Science Department Of Computer Science Hiroshima City University
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