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On the Number of Two-Weight Cyclic Codes with Composite Parity-Check Polynomials

  • Gerardo Vega
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5130)

Abstract

Sufficient conditions for the construction of a two-weight cyclic code by means of the direct sum of two one-weight cyclic codes, were recently presented in [4]. On the other hand, an explicit formula for the number of one-weight cyclic codes, when the length and dimension are given, was proved in [3]. By imposing some conditions on the finite field, we now combine both results in order to give a lower bound for the number of two-weight cyclic codes with composite parity-check polynomials.

Keywords

One-weight cyclic codes two-weight cyclic codes 

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References

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    Lidl, R., Niederreiter, H.: Finite Fields. Cambridge Univ. Press, Cambridge (1983)zbMATHGoogle Scholar
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    MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes, Amsterdam. North-Holland, The Netherlands (1977)zbMATHGoogle Scholar
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    Vega, G.: Determining the Number of One-weight Cyclic Codes when Length and Dimension are Given. In: Carlet, C., Sunar, B. (eds.) WAIFI 2007. LNCS, vol. 4547, pp. 284–293. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Vega, G.: Two-weight cyclic codes constructed as the direct sum of two one-weight cyclic codes, Finite Fields Appl. (in press, 2008), doi:10.1016/j.ffa.2008.01.002Google Scholar
  5. 5.
    Wolfmann, J.: Are 2-Weight Projective Cyclic Codes Irreducible? IEEE Trans. Inform. Theory. 51, 733–737 (2005)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Gerardo Vega
    • 1
  1. 1.Dirección General de Servicios de Cómputo AcadémicoUniversidad Nacional Autónoma de MéxicoMéxico D.F.Mexico

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