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The split weight (w L , w R ) enumeration of Reed-Muller codes for w L +w R <2d min

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1255))

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Abstract

Formulas for the distributions of split weights (w L , w R ) of Reed-Muller codes are presented for w L +w r less than twice the minimum weight d min. A canonical form for all the relevant Boolean polynomials is derived. These results are applied to analyzing the structure and complexity of subtrellises of codewords of weights less than 2d min of Reed-Muller codes.

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References

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Author information

Authors and Affiliations

  1. Graduate School of Information Science, Nara Institute of Science and Technology, 8916-5 Takayama-cho, Ikoma, 630-01, Nara, Japan

    Tadao Kasami & Tsukasa Sugita

  2. Graduate School of Engineering Sciences, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, 560, Osaka, Japan

    Toru Fujiwara

Authors
  1. Tadao Kasami
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  2. Tsukasa Sugita
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  3. Toru Fujiwara
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Editor information

Teo Mora Harold Mattson

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© 1997 Springer-Verlag Berlin Heidelberg

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Kasami, T., Sugita, T., Fujiwara, T. (1997). The split weight (w L , w R ) enumeration of Reed-Muller codes for w L +w R <2d min . In: Mora, T., Mattson, H. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1997. Lecture Notes in Computer Science, vol 1255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63163-1_16

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  • DOI: https://doi.org/10.1007/3-540-63163-1_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63163-7

  • Online ISBN: 978-3-540-69193-8

  • eBook Packages: Springer Book Archive

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