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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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Book cover 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

  1. T. Sugita, T. Kasami, and T. Fujiwara, “A Method for Computing Split Weight Distributions of Reed-Muller Codes,” Proc. of the International Symposium on Information Theory and Its Applications, pp.598–601, Victoria, Canada, Sep. 1996.

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  2. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, Amsterdam, The Netherlands: North-Holland, 1977.

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  3. T. Kasami and N. Tokura, “On the Weight Structure of Reed-Muller Codes,” IEEE Trans. Information Theory, Vol. 16, No.6, pp. 752–759, Nov. 1970.

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  4. H.T. Moorthy, S. Lin and T. Kasami, “Soft-Decision Decoding of Binary Linear Block Codes Based on an Iterative Search Algorithm,” Proc. of IEEE International Symposium on Information Theory, p.474, Whistler, Canada, Sep. 1995, also to appear in IEEE Trans. Information Theory.

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  5. T. Koumoto, T. Takata, T. Kasami, and S. Lin, “An Iterative Soft-Decision Decoding Algorithm,” Proc. of the International Symposium on Information Theory and Its Applications, pp.806–810, Victoria, Canada, Sep. 1996.

    Google Scholar 

  6. G.D. Forney, Jr.,“Dimension/Length Profiles and Trellis Complexity of Linear Block Codes,” IEEE Trans. Information Theory, Vol. 40, No.6, pp. 1742–1752, Nov. 1994.

    Google Scholar 

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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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