More permutation polynomials with Niho exponents which permute Fq2

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 F-p2k with Niho exponents of the form f(x) = x + lambda(1)x(s(pk-1)+1) + lambda(2)x(t(pk -1)+1); some necessary and sufficient conditions for the polynomial f(x) to permute F-p2k are provided. Specifically, for p = 5, new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials. (C) 2019 Elsevier Inc. All rights reserved.