Collection of Polynomials over Finite Fields Providing Involutary Permutations

Abstract

For an odd prime power $q$ satisfying $q\equiv 1\pmod 3$ we construct totally $2(q-1)$ permutation polyomials, all giving involutory permutations with exactly $1+ \frac{q-1}3$ fixed points. Among them $(q-1)$ polynomials are trinomials, and the rest are 6-term polynomials.Comment: 10 pages; Comments welcome