Several new permutation quadrinomials over finite fields of odd characteristic

摘要

Let F-q denote the finite field with q elements. In this paper, we study the permutation property of the polynomial x(3) + ax(q+2) + bx(2q+1) + cx(3q) is an element of F-q2 [x], where char F-q = 3, 5. More precisely, for a, b, c is an element of F-q*, we propose eight new classes of permutation quadrinomials of the form x(3) + ax(q+2) + bx(2q+1) + cx(3q) is an element of F-q2 [x] for q = 3(m), and three new classes of permutation quadrinomials of the form x(3) + ax(q+2) + bx(2q+1) + cx(3q) is an element of F-q2 [x] for q = 5(m).