Determination of a type of permutation binomials over finite fields

By Xiang-dong Hou, Stephen D. Lappano. 2013

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Abstract Let f = a x + x 3 q − 2 ∈ F q 2 [ x ] , where a ∈ F q 2 ⁎ . We prove that f is a permutation polynomial of F q 2 if and only if one of the following occurs: (i) q = 2 e , e odd, and a q + 1 3 is a primitive 3rd root of unity. (ii) ( q , a ) belongs to a finite set which is determined in the paper.

Subfields: Artificial Intelligence, Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/0d8938a0949ef22567b68a0652d1bcae4161bb3a