Weight Distribution of Some Cyclic Codes of MacWilliams

  • V. K. Bhargava
  • C. Nguyen

Abstract

Mrs. MacWilliams recently gave methods for the decomposition of cyclic codes of block lengths 3p, 5p, and 7p into systematic quasi-cyclic form. In this paper, using her results, we construct and enumerate the complete weight distribution of many cyclic codes. Among the many codes, exhibiting remarkable gaps in their weight distributions are the (87,28,24), (51,16,16) and the (91,12,36) codes with weights divisible by four, and a (85,16,32) code with weights divisible by eight. We also report on a (52,13, 16) quasi-cyclic subcode (of the (65,13,25) cyclic code) with all weights divisible by four. It is not known if this code is cyclic as well.

Keywords

Stein 

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References

  1. (1).
    MacWilliams, F.J.: 1979, “Decomposition of cyclic codes of block lengths 3p,5p,7p”, IEEE Trans on Info. Theory, 25,Google Scholar
  2. (2).
    Karlin, M.: 1970, “Decoding of circulant codes”, IEEE Trans. on Info. Theory, l6,pp. 797–802.MathSciNetCrossRefGoogle Scholar
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    Bhargava, V.K., Séguin, G.E., and Stein, J.M.: 1978, “Some (mk,k) cyclic codes in quasi-cyclic form”, IEEE Trans. on Info. Theory, 24, pp. 630–632.MATHCrossRefGoogle Scholar
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    Pieper, J.F., Proakis, J.G., Reed, R.R., and Wolf, J.K.: 1978, “Design of Efficient Coding and Modulation for a Rayleigh Fading Channel”, IEEE Trans. on Info. Theory, 24,pp. 457–469.MATHCrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1980

Authors and Affiliations

  • V. K. Bhargava
    • 1
  • C. Nguyen
    • 2
  1. 1.Dept. Elec. Eng.Concordia UniversityMontrealCanada
  2. 2.Canadian Marconi CompanyMontrealCanada

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