Several Classes of Permutation Trinomials over ${\mathbb{F}}_{5^n}$ From Niho Exponents

Abstract

The construction of permutation trinomials over finite fields attracts people's interest recently due to their simple form and some additional properties. Motivated by some results on the construction of permutation trinomials with Niho exponents, by constructing some new fractional polynomials that permute the set of the $(q+1)$-th roots of unity in ${\mathbb{F}}_{q^2}$, we present several classes of permutation trinomials with Niho exponents over ${\mathbb{F}}_{q^2}$, where $q=5^k$.