Permutation and local permutation polynomial of maximum degree

08/02/2023

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by   Jaime Gutierrez, et al.

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Let F_q be the finite field with q elements and F_q[x_1,…, x_n] the ring of polynomials in n variables over F_q. In this paper we consider permutation polynomials and local permutation polynomials over F_q[x_1,…, x_n], which define interesting generalizations of permutations over finite fields. We are able to construct permutation polynomials in F_q[x_1,…, x_n] of maximum degree n(q-1)-1 and local permutation polynomials in F_q[x_1,…, x_n] of maximum degree n(q-2) when q>3, extending previous results.