Permutation trinomials over \mathbbF_q³

2018/04/04 by Daniele Bartoli, Bartoli, Daniele
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #math.CO

paper · pdf · doi:10.48550/arxiv.1804.01305

arxiv created 2018/04/04 · openalex publication_date 2018/04/04 · arxiv updated 2018/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider four classes of polynomials over the fields \mathbbF_q³, q=p^h, p>3, f₁(x)=x^q2+q-1+Ax^q2-q+1+Bx, f₂(x)=x^q2+q-1+Ax^q3-q2+q+Bx, f₃(x)=x^q2+q-1+Ax^q2-Bx, f₄(x)=x^q2+q-1+Ax^q-Bx, where A,B ∈ \mathbbF_q. We determine conditions on the pairs (A,B) and we give lower bounds on the number of pairs (A,B) for which these polynomials permute \mathbbF_q³.

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