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Self-dual codes 2n circulant over Fq (q=2r)

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Algebraic Algorithms and Error-Correcting Codes (AAECC 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 229))

Abstract

We give a constructive characterization of all self dual 2n circulant codes over F2r. This construction generalizes those of F. J. MacWilliams [3], and G.F.M. Beenker [1]. Our method is original. We also give the number of these codes, as well as an outline of an algorithm to construct them. At last, we give several codes we have obtained by software at AAECC Lab.

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References

  1. G.F. Beenker “On double circulant codes” T.H. Report 80, WSK 04 July 1980

    Google Scholar 

  2. M. Karlin “New binary coding results by circulants” IEEE trans. info. Theory, 15, (1969), 797–802

    Google Scholar 

  3. J.S. Leon,J.M. Masley,V. Pless “On weights in duadic codes” Abstract of papers, IEEE june 24–28, (1985), Brighton, U.K.

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  4. F.J. MacWilliams “Orthogonal circulant matrices over finite fields” J. of Comb. Theory, 10, 1971, 1–17

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  5. F.J. MacWilliams,N.J.A. Sloane “The theory of error correcting codes” North Holland Mathematic Library, vol. 16, 1977

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  6. A. Poli “Codes dans certaines algèbres modulaires” Thèse d'état, Univ. P. Sabatier, Toulouse, FRANCE, 1978

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  7. A. Poli “Idéaux principaux nilpotents de dimension maximale dans l'algèbre Fq[G] d'un groupe abélien” Com. in Algebra, vol. 12, no 3 et 4, (1984), 391–401

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  8. A. Poli “Construction of primitive idempotents for n variable codes” Acts of AAECC-2 Coll., Toulouse 1984, (submitted for p. Spring. Ver.)

    Google Scholar 

  9. M. Ventou “Contribution à l'étude des codes polynomiaux” Thèse de 3ème cycle, Univ. P. Sabatier, Toulouse, FRANCE, 1984

    Google Scholar 

  10. M. Ventou, C. Rigoni “Self dual doubly circulant codes” Discrete Math., 56 vol. 1,2 (1985)

    Google Scholar 

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Authors and Affiliations

  1. AAECC Lab., Univ. P. Sabatier, 31062, Toulouse, France

    A. Poli & C. Rigoni

Authors
  1. A. Poli
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  2. C. Rigoni
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Editor information

Jacques Calmet

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© 1986 Springer-Verlag Berlin Heidelberg

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Poli, A., Rigoni, C. (1986). Self-dual codes 2n circulant over Fq (q=2r). In: Calmet, J. (eds) Algebraic Algorithms and Error-Correcting Codes. AAECC 1985. Lecture Notes in Computer Science, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16776-5_722

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  • DOI: https://doi.org/10.1007/3-540-16776-5_722

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16776-1

  • Online ISBN: 978-3-540-39855-4

  • eBook Packages: Springer Book Archive

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