Eurocode ’92 pp 135-146 | Cite as

Bound for Trace-Equation and Application to Coding Theory

  • V. Gillot
Part of the International Centre for Mechanical Sciences book series (CISM, volume 339)


Using the vector space structure of finite field extension of characteristic two, we transform a one-variable polynomial into a two-variable one. Applying the Deligne bound about exponential sums [1] to the two-variable polynomial, we improve in several cases the bound on the number of solutions for trace-equation. In this way, we obtain different results in Coding Theory. Using the trace-description of the codewords for cyclic codes introduced by Wolfmann [6], we improve the bound on weights for these codes and we also generalize, in different cases, the results of Moreno and Kumar in [2].


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    P. KUMAR AND O. MORENO, “Minimum distance bounds for cyclic codes and Deligne’s theorem”, preprint.Google Scholar
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    J. WOLFMANN, “Polynomial description of binary linear codes and related properties”, A.A.E.C.C., 2, pp 119–138 (1991).zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • V. Gillot
    • 1
  1. 1.University of Toulon and VarLa GardeFrance

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