The Weight Distributions of Cosets of the Second-Order Reed-Muller Code of Length 128 in the Third-Order Reed-Muller Code of Length 128

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概要

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• In this paper, cosets of the second order Reed-Muller code of length 2^m, denoted RM_<:m,2>, in the third order Reed-Muller code of the same length, denoted RM_<m,3>, are studied. The set of cosets, RM_<m,3>/RM_<m,2> is partitioned into blocks. Two cosets are in the same block, if and only if there is a transformation in the general linear group by which one coset is transformed into the other. Two cosets in the same block have the same weight distribution. For the code length less than or equal to 128, the representative coset leader of each block is presented and the weight distribution of cosets in the block is computed. By using these results, the extended code of a cyclic code of length 128 between RM_<7,2> and RM_<7,3> can be decomposed into a set of cosets in RM_<7,3>/RM_<7,2>, and its weight distribution can be derived. Several cyclic codes of length 127 are shown to be equivalent and some new linear unequal error protection codes are found.

• 社団法人電子情報通信学会の論文
• 1996-04-25

著者

• Fujiwara Toru

  Osaka University

• Fujiwara T

  Osaka University

• Fujiwara Toru

  Department Of Multimedia Engineering Graduate School Of Information Science And Technology Osaka Uni

• KASAMI Tadao

  Graduate School of Information Science, Nara Institute of Science and Technology

• Fujiwara Toru

  Faculty of Engineering Science, Osaka University

• Desaki Yoshihisa

  Faculty of Engineering Science, Osaka University

• Kasami Tadao

  Graduate School Of Information Science Nara Institute Of Science And Technology

• Koumoto Takuya

  Okayama University

• Fujiwara Toru

  Faculty Of Engineering Science Osaka University

• Fujiwara T

  Department Of Multimedia Engineering Graduate School Of Information Science And Technology Osaka Uni

• Koumoto T

  Hiroshima City Univ. Hiroshima Jpn

• Desaki Y

  The Department Of Electronics And Information Engineering Faculty Of Engineering Tokyo Metropolitan

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