A class of permutation polynomials over the group ring F_pC_p^n

Abstract

Let p be a prime number and F_pC_p^n denote the group ring of a cyclic group of order pn over Fp. We study the permutation property of the polynomial a_0 + a_1x + a_px^p + · · · + a_p^n x^(p^n) with coefficients a_i ∈ F_pC_p^n where i = 0, 1, p, . . . , p^n. Necessary and sufficient conditions on the coefficients have been obtained so that it becomes a permutation polynomial.