Bound for Trace-Equation and Application to Coding Theory
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  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 , we improve the bound on weights for these codes and we also generalize, in different cases, the results of Moreno and Kumar in .
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