Regular complete permutation polynomials over quadratic extension fields

2022/12/28 by Lu, Wei, Wu, Xia, Wang, Yufei +1
#94A62 #94B05 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2212.13674

Abstract

Let r≥ 3 be any positive integer which is relatively prime to p and q²≡ 1 \pmod r. Let τ₁, τ₂ be any permutation polynomials over \mathbbF_q², σ_M is an invertible linear map over \mathbbF_q² and σ=τ₁∘σ_M∘τ₂. In this paper, we prove that, for suitable τ₁, τ₂ and σ_M, the map σ could be r-regular complete permutation polynomials over quadratic extension fields.

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