Regular complete permutation polynomials over quadratic extension fields

Abstract

Let r ≥ 3 be any positive integer which is relatively prime to p and q 2 ≡ 1 (mod r). Let τ 1 , τ 2 be any permutation polynomials over F q 2 , σ M is an invertible linear map over F q 2 and σ = τ 1 • σ M • τ 2 . In this paper, we prove that, for suitable τ 1 , τ 2 and σ M , the map σ could be r-regular complete permutation polynomials over quadratic extension fields. 2020 Mathematics Subject Classification. 94B05.