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Bound for Trace-Equation and Application to Coding Theory

Abstract : 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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Valérie Gillot. Bound for Trace-Equation and Application to Coding Theory. Camion, P. and Charpin, P. and Harari, S. Eurocode '92, International Symposium on Coding Theory and Applications, 339, Springer Vienna, pp.135-146, 1993, 978-3-211-82519-8. ⟨10.1007/978-3-7091-2786-5_12⟩. ⟨hal-00993194⟩



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