## Estimates for the Mixed Exponential Sum Associated to Polynomials Over F2m

##### Author

Molina Gonzalez, Braulio

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In this thesis, we addressed the open problem of improving the bound for mixed exponential
sum associated to polynomials over F2m (Theorem 3.0.2), for some polynomials of
large degree i.e. (when compared to m). In order to do this, such polynomials will have to
be predetermined by the zeros of binary cyclic codes. This is accomplish by extending a
result of T. Cochrane & C. Pinner [1] for the bound of such sums from the fields of prime
order, to the fields of order a power of two. The bound of this principal result (Theorem
7.0.1) depends on the number of solutions of systems of polynomial equations, for which
we employ results of coding theory to find the exact number of solutions in such equations,
thus improving the bound (Theorem 3.0.2) for such polynomials of large degree.