On monomial exponential sums in certain index 2 cases and their connections to coding theory

Abstract

<div lang="en" class="abs"><p class="abs_header">Abstract</p><p>In this paper monomial exponential sums over finite fields in certain index 2 cases are considered. A recursion is given to compute these sums for most values of the parameters. For the remaining values we should know certain Gauss sums exactly, which seems to be a hard problem in general. Examples illustrating the methods and the remaining difficulties are given. Also, computational data is given showing what happens for small values of the parameters.</p></div>