New results of sparse permutation polynomials with trace functions over 𝔽_q^n

Permutation polynomials with sparse forms over finite fields attract researchers’ great interest and have important applications in many areas of mathematics and engineering. In this paper, by investigating the exponents (s, i) and the coefficients a,b∈𝔽_q^* , we present some new results of permutation polynomials of the form f(x)= ax^q^i(q^2-q+1) + bx^s + Tr_q^n/q(x) over 𝔽_q^n ( n=2 or 3). The permutation property of the new results is given by studying the number of solutions of special equations over 𝔽_q^n .