More permutation polynomials with Niho exponents which permute [formula omitted

Abstract

Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over Fp2k with Niho exponents of the form f(x)=x+λ1xs(pk−1)+1+λ2xt(pk−1)+1; some necessary and sufficient conditions for the polynomial f(x) to permute Fp2k are provided. Specifically, for p=5, new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials.