<abstract xmlns="http://www.w3.org/1999/xhtml">
In this paper, we first give a relationship between generalized algebraic geometry codes (GAG codes) and algebraic geometry codes (AG codes). More precisely, we show that a GAG code is contained (up to isomorphism) in a suitable AG code. Next we recall the concept of an <italic>N</italic>1<italic>N</italic>2-automorphism group, a subgroup of the automorphism group of a GAG code. With the use of the relation we obtained between these two classes of codes, we show that the <italic>N</italic>1<italic>N</italic>2-automorphism group is a subgroup of the automorphism group of an AG code.
</abstract>

In this paper, we first give a relationship between generalized algebraic geometry codes (GAG codes) and algebraic geometry codes (AG codes). More precisely, we show that a GAG code is contained (up to isomorphism) in a suitable AG code. Next we recall the concept of an N1N2-automorphism group, a subgroup of the automorphism group of a GAG code. With the use of the relation we obtained between these two classes of codes, we show that the N1N2-automorphism group is a subgroup of the automorphism group of an AG code.

On a relation between GAG codes and AG codes

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On a relation between GAG codes and AG codes"}

In this paper, we first give a relationship between generalized algebraic geometry codes (GAG codes) and algebraic geometry codes (AG codes). More precisely,...

On a relation between GAG codes and AG codes

Published Online: Oct 21, 2023

Page range: 221 - 227

Received: Sep 10, 2022

Accepted: Dec 20, 2022

DOI: https://doi.org/10.2478/auom-2023-0040

Keywords
Algebraic geometry codes, generalized algebraic geometry codes, geometric Goppa codes, code automorphisms, algebraic function fields

© 2023 Engin Şenel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On a relation between GAG codes and AG codes

Published Online: Oct 21, 2023

Page range: 221 - 227

Received: Sep 10, 2022

Accepted: Dec 20, 2022

DOI: https://doi.org/10.2478/auom-2023-0040

KeywordsAlgebraic geometry codes, generalized algebraic geometry codes, geometric Goppa codes, code automorphisms, algebraic function fields

© 2023 Engin Şenel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Algebraic geometry codes, generalized algebraic geometry codes, geometric Goppa codes, code automorphisms, algebraic function fields