Character sum; Exponential sum; Permutation Polynomial; Almost Perfect Nonlinear Function; Finite Field
In the second half of the 1990s Christian Mauduit and András Sárközy  introduced a new quantitative theory of pseudorandomness of binary sequences. Since then numerous papers have been written on this subject and the original theory has been generalized in several directions. Here I give a survey of some of the most important results involving the new quantitative pseudorandom measures of finite bi-nary sequences. This area has strong connections to finite fields, in particular, some of the best known constructions are defined using characters of finite fields and their pseudorandom measures are estimated via character sums.
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