Cyclotomic function fields over finite fields with irreducible quadratic modulus

2023/09/11 by Nazar Arakelian, Arakelian, Nazar, Luciane Quoos +1
Computer Science · #Algebraic Geometry (math.AG) #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2309.05424

openalex publication_date 2023/09/11 · openalex created_date 2023/09/13 · openalex updated_date 2026/07/28

Abstract

Let \mathbbF_q be the finite field of order q and F=\mathbbF_q(x) the rational function field. In this paper, we give a characterization of the cyclotomic function fields F(Λ_M) with modulus M, where M ∈ \mathbbF_q[T] is a monic and irreducible polynomial of degree two. We also provide the full automorphism group of F(Λ_M) in odd characteristic, extending results of \citeMXY2016 where the automorphism group of F(Λ_M) over \mathbbF_q was computed.

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