Existence of primitive normal pairs over finite fields with prescribed subtrace

2024/05/19 by Kajari Chatterjee, Chatterjee, K., Giorgos Kapetanakis +5
Computer Science · Mathematics · #11T23 #12E20 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.11463

openalex publication_date 2024/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given positive integers q,n,m and a∈\mathbbF_q, where q is an odd prime power and n≥ 5, we investigate the existence of a primitive normal pair (ε,f(ε)) in \mathbbF_qⁿ over \mathbbF_q such that STr_qⁿ/q(ε)=a, where f(x)=\fracf₁(x)f₂(x)∈\mathbbF_qⁿ(x) is a rational function together with deg(f₁)+deg(f₂)=m and STr_qⁿ/q(ε) = ∑_0≤ i

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