Abstract
In this paper we extend the covering method for computing the exact 2-divisibility of exponential sums of Boolean functions, improve results on the divisibility of the Hamming weight of deformations of Boolean functions, and provide criteria to obtain non-balanced functions. In particular, we present criteria to determine cosets of Reed-Muller codes that do not contain any balanced function, and to construct deformations of symmetric functions that are not balanced. The use of the covering method together with classifications of cosets of Reed-Muller codes obtained by the action of linear groups can improve the search of balanced functions in Reed-Muller codes dramatically.
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