An algebraic construction of generalized Beenker's codes

  • Alain Poli
  • Mostafa Belkasmi
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 539)


We propose an algebraic construction for codes which are GF(q)-images of Abelian codes over GF(qm). These codes generalize the Beenker's codes [1] and the Poli's one [6,p.285–295].

The construction here is quite different from that of Beenker and from that of Poli.


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  1. [1]
    G.F.M. Beenker, On double circulant codes, report 80-WSK-04, Technological University Eindhoven (1980).Google Scholar
  2. [2]
    G.F.M. Beenker, A Note on the extended Quadratic Residue codes over GF(9) and their ternary images, IEEE Trans. Inform. Theory, vol.IT-30, no.2, (1984), 403–405.Google Scholar
  3. [3]
    F.J. MacWilliams, Orthogonal circulant matrices over finite fields and how to find them, J. Comb. Theory 10, (1971), 1–17.Google Scholar
  4. [4]
    M. Karlin, New binary codes results by circulant, IEEE Trans. Inform. Theory, vol.IT-15, (1969), 81–92.Google Scholar
  5. [5]
    M. Karlin, Decoding of circulant codes, IEEE Trans. Inform. Theory, vol.IT-16, (1970), 797–802.Google Scholar
  6. [6]
    A. Poli et L. Huguet, Codes correcteurs: théorie et applications, (PARIS:MASSON 1989).Google Scholar
  7. [7]
    A. Poli, Construction of SDMC codes over GF(2) or GF(3), LNCS Springer, no.307, (1988), 130–139.Google Scholar
  8. [8]
    A. Poli, Some algebraic tools for error correcting codes, LNCS Springer, no.227, (1986), 43–61.Google Scholar
  9. [9]
    T. Verhoeff, An updated table of minimum-distance bounds for binary linear codes, IEEE Trans. Inform. Theory, vol.IT-33, no.5, (1987), 665–680.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Alain Poli
    • 1
  • Mostafa Belkasmi
    • 1
  1. 1.Laboratoire AAECC/LSI, IRITUniversité Paul SabatierToulouse cedexFrance

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