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.

Cited by in corpus (3)

• On the constructions of $n$-cycle permutations
• A new class of permutation trinomials constructed from Niho exponents
• More new classes of permutation trinomials over ${\mathbb{F}}_{2^n}$