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On the automorphisms of generalized algebraic geometry codes

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Abstract

We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of \(N_1N_2\)-automorphism group of a GAG code in this class-that is, a subgroup of the automorphism group of the code. Then we determine a subgroup of the \(N_1N_2\)-automorphism group in the general case and the \(N_1N_2\)-automorphism group itself in the rational function field case. We also explicitly construct such a group. This paper presents a method to obtain similar results for the GAG codes that have more collections of places of the same degree in their construction.

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  1. Department of Mathematics, Trakya University, 22030, Edirne, Turkey

    Engin Şenel & Figen Öke

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  1. Engin Şenel
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  2. Figen Öke
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All authors contributed to the study conception and design. The first draft of the manuscript was written by Engin Şenel and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Engin Şenel.

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Communicated by J. W. P. Hirschfeld.

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Şenel, E., Öke, F. On the automorphisms of generalized algebraic geometry codes. Des. Codes Cryptogr. 90, 1369–1379 (2022). https://doi.org/10.1007/s10623-022-01043-1

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