On components of vectorial permutations of F_q~n

摘要

We consider vectorial mapsF(x(1), ..., x(n)) = (f(1) (x(1), ..., x(n)), ..., f(n) (x(1), ..., x(n))) : F-q(n) bar right arrow F-q(n),which induce permutations of F-q(n) . We show that the degrees of the components f(1), f(2), ..., f(n) is an element of F-q [x(1), ..., x(n)] are at least 2 when 2 = deg(F) = d root q and d vertical bar (q - 1) Our proof uses an absolutely irreducible curve over F-q and the number of rational points on it that we relate to the cardinality of the value set of a polynomial. (C) 2019 Elsevier Inc. All rights reserved.