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arXiv · 2511.21292

The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry codes

Xubin Hu·Liming Ma
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Abstract

In this manuscript, we investigate the automorphism group of a maximal function field with the second largest possible genus over finite field of even characteristic, which is called the Abdón--Torres function field. As an application, we determine the automorphism groups of one-point algebraic geometry codes from such a maximal function field. It turns out that the automorphism groups of one-point algebraic geometry codes agree with that of the Abdón--Torres function field except for the trivial cases. Moreover, we provide a family of maximal function fields with explicit defining equations via considering fixed subfields with respect to some subgroups of automorphism group of the Abdón--Torres function field.

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Xubin Hu, Liming Ma. 2025-11-26. The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry codes. https://arxiv.org/abs/2511.21292

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