# Regular complete permutation polynomials over quadratic extension fields

Let r≥ 3 be any positive integer which is relatively prime to p and q^2≡ 1 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.

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