New results on permutation polynomials of the form ( x p m − x + δ ) s + x p m + x over 𝔽 p 2m

Abstract

Permutation polynomials over finite fields have significant applications in coding theory, cryptography, combinatorial designs and many other areas of mathematics and engineering. In this paper, we study the permutation behavior of polynomials with the form \((x^{p^{m}}-x+\delta )^{s}+x^{p^{m}}+x\) over the finite field \(\mathbb {F}_{p^{2m}}\) . By using the Akbary-Ghioca-Wang (AGW) criterion, we present several new classes of permutations over \(\mathbb {F}_{p^{2m}}\) based on some bijections over the set \(\{t\in \mathbb {F}_{p^{2m}}|t^{p^{m}}+t=0\}\) or the subfield \(\mathbb {F}_{p^{m}}\) .

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