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].
Type de document :
Chapitre d'ouvrage
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〉
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https://hal.inria.fr/hal-00993194
Contributeur : Valérie Gillot <>
Soumis le : lundi 19 mai 2014 - 18:27:48
Dernière modification le : mardi 19 juin 2018 - 15:50:01

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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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