Two classes of permutation polynomials with Niho exponents over finite fields with even characteristic

Authors: QIAN LIU

Abstract: In this paper, by transforming the permutation problem into the root distribution problem in the unit circle of certain quadratic and cubic equations, we investigate the permutation behavior of the type $f(x)=x+x^{2^{3m}-2^m+1}+x^{2^{4m}-2^{3m}+2^m}$ over $F_{2^{4m}}$ and $f(x)=x+x^{2^m}+x^{2^{m+1}-1}+ax^{2^{2m}-2^m+1}$ over $F_{2^{2m}}$, respectively.

Keywords: Finite field, permutation trinomial, permutation quadrinomial

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