On some Galois covers of the Suzuki and Ree curves

2016/09/29 by Massimo Giulietti, Maria Montanucci, Giulietti, Massimo +5 · 1 citation
Computer Science · Mathematics · #14H37 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1609.09343

openalex publication_date 2016/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the full automorphism group of two recently constructed families S_q and R_q of maximal curves over finite fields. These curves are covers of the Suzuki and Ree curves, and are analogous to the Giulietti-Korchmáros cover of the Hermitian curve. We also show that S_q is not Galois covered by the Hermitian curve maximal over \mathbbF_q⁴, and R_q is not Galois covered by the Hermitian curve maximal over \mathbbF_q⁶. Finally, we compute the genera of many Galois subcovers of S_q and R_q; this provides new genera for maximal curves.

Cited by

• Uniqueness of Skabelund Maximal Curves via Genus and Automorphism Groups

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