A characterization and an explicit description of all primitive polynomials of degree two over finite fields

2024/09/02 by Gerardo Vega, Vega, Gerardo
Computer Science · #11T71 #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #General Mathematics (math.GM) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2409.17147

openalex publication_date 2024/09/02 · openalex created_date 2024/10/28 · openalex updated_date 2026/07/28

Abstract

For polynomials of degree two over finite fields, we present an improvement of Fitzgerald's characterization (Finite Fields Appl. 9(1):117-121, 2003). We then use this new characterization to obtain an explicit, complete, and simple description of all primitive polynomials of degree two over finite fields.

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