Permutation trinomials over ${\mathbb{F}}_{2^m}$: a corrected version

Abstract

Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we determine all permutation trinomials over ${\mathbb{F}}_{2^m}$ in Zieve's paper. We prove a conjecture proposed by Gupta and Sharma and obtain some new permutation trinomials over ${\mathbb{F}}_{2^m}$. Finally, we show that some classes of permutation trinomials with parameters are QM equivalent to some known permutation trinomials.

References in corpus (2)

• On some permutation polynomials over F_q of the form x^r*h(x^((q-1)/d)))
• New Classes of Permutation Binomials and Permutation Trinomials over Finite Fields

Cited by in corpus (9)

• On Inverses of Permutation Polynomials of Small Degree over Finite Fields
• On inverses of some permutation polynomials over finite fields of characteristic three
• On the constructions of $n$-cycle permutations
• Some new classes of permutation polynomials and their compositional inverses
• More constructions of $n$-cycle permutations
• A conjecture on permutation trinomials over finite fields of characteristic two
• More new classes of permutation trinomials over ${\mathbb{F}}_{2^n}$
• Permutation polynomials over finite fields from low-degree rational functions
• A new class of permutation trinomials constructed from Niho exponents