Four new classes of permutation trinomials and their compositional inverses

2025/05/04 by Sartaj Ul Hasan, Ramandeep Kaur, Hasan, Sartaj Ul +2
Computer Science · Decision Sciences · Engineering · #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2505.02128

openalex publication_date 2025/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct four new classes of permutation trinomials over the cubic extension of a finite field with even characteristic. Additionally, we explicitly provide the compositional inverse of each class of permutation trinomials in polynomial form. Furthermore, we derive the compositional inverse of the permutation trinomial αX^{q(q2 - q + 1)} + βX^{q2 - q + 1} + 2X for α= 1 and β= 1, originally proposed by Xie, Li, Xu, Zeng, and Tang (2023).

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