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Construction of SDMC codes over GF (2) or GF (3)

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Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra (AAECC 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 307))

Abstract

We give a complete algorithm to construct every possible bordered SDMC codes with coefficients in GF(2) or GF(3). Several new proofs are developed too.

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References

  1. Beenker GMF "On double circulant codes" TH. Report 80, WSK-04, 1980,Univ.Eindhoven.The Need.

    Google Scholar 

  2. Berlekamp ER "Algebraic coding theory" Mac Graw Hills, NY,1968

    Google Scholar 

  3. Karlin M "New binary coding results by circulants" IEEE Trans. on Inf.Th.,vol 15,pp797–802,1969.

    Google Scholar 

  4. Karlin M "Decoding of circulant codes" IEEE Trans. on Inf.Th.,pp797–802,Nov.1970.

    Google Scholar 

  5. Leech J "Some sphere packing in higher space". Can. J. of Math.,pp657–682,1964.

    Google Scholar 

  6. MacWilliams FJ "Orthogonal circulant matrices over finite fields and how to find them" J. of Comb. Th.,vol.10,pp1–17,1971.

    Google Scholar 

  7. MacWilliams FJ Sloane NJA "The theory of error correcting codes" North Holland Math. Lib.,3ndEdit.,1981.

    Google Scholar 

  8. Malliavin MP "Les groupes finis et leurs représentations complexes" Masson,NY,1981.

    Google Scholar 

  9. Poli A "Idéaux principaux nilpotents de dimension maximale dans FqG algèbre de groupe abélien fini". Comm. in Algebra,12(4),pp391–401,1984.

    Google Scholar 

  10. Poli A "Construction of primitive idempotents for n variable codes" Lect. Notes, in Comp. Sc., Springer no228, pp 25–35 1986

    Google Scholar 

  11. Poli A "Multi-circulant codes over Fq" Submitted to Comm. in Algebra.

    Google Scholar 

  12. Poli A,Rigoni C "Enumeration of self dual 2k circulant codes" Lect. Notes,in Comp. Sc., Springer no228, pp61–71, 1986.

    Google Scholar 

  13. Poli A,Rigoni C "Self dual codes 2n circulant over Fq (q=2r)". Lect. Notes in Comp. Sc., Springer no 229,pp194–201

    Google Scholar 

  14. Ventou M,Rigoni "Self dual doubly circulant codes" Discrete Math.,vol.56,pp291–298,1985.

    Google Scholar 

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Author information

Authors and Affiliations

  1. AAECC/LSI, University P. Sabatier, 118 route de Narbonne, 31072, Toulouse cédex, France

    A. Poli

Authors
  1. A. Poli
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Thomas Beth Michael Clausen

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© 1988 Springer-Verlag Berlin Heidelberg

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Poli, A. (1988). Construction of SDMC codes over GF (2) or GF (3). In: Beth, T., Clausen, M. (eds) Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra. AAECC 1986. Lecture Notes in Computer Science, vol 307. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039187

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  • DOI: https://doi.org/10.1007/BFb0039187

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19200-8

  • Online ISBN: 978-3-540-39133-3

  • eBook Packages: Springer Book Archive

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