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Equality and iso-duality of Generalized Geometric Goppa codes

  • Jyoti Dasgupta
  • Nupur Patanker
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Abstract

Geometric Goppa codes are constructed by evaluating elements of an algebraic function field at the places of degree one. Extending this, generalized geometric Goppa codes were defined in [XNL99] and [Hey02] by allowing evaluation at places of arbitrary degree. In this paper, we establish necessary and sufficient conditions for equality of generalized geometric Goppa codes, following the approach of [MP93]. These conditions serve as a key tool in our characterization of iso-dual and self-dual generalized geometric Goppa codes. Given a separable extension M/F of algebraic function fields and an iso-dual generalized geometric Goppa code over F, we extend the construction of [CPQT24] to obtain iso- dual generalized geometric Goppa codes over M. Furthermore, we study self-duality of generalized AG codes ([XNL99], [DM03]).

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Cite

BibTeXRIS
BibTeX
@misc{dasgupta2026equality,
  title = {{Equality and iso-duality of Generalized Geometric Goppa codes}},
  author = {Jyoti Dasgupta and Nupur Patanker},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25740},
  eprint = {2609.25740},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25740},
}
RIS
TY  - UNPB
TI  - Equality and iso-duality of Generalized Geometric Goppa codes
AU  - Jyoti Dasgupta
AU  - Nupur Patanker
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25740
UR  - https://arxiv.org/abs/2609.25740
AB  - Geometric Goppa codes are constructed by evaluating elements of an algebraic function field at the places of degree one. Extending this, generalized geometric Goppa codes were defined in [XNL99] and [Hey02] by allowing evaluation at places of arbitrary degree. In this paper, we establish necessary and sufficient conditions for equality of generalized geometric Goppa codes, following the approach of [MP93]. These conditions serve as a key tool in our characterization of iso-dual and self-dual generalized geometric Goppa codes. Given a separable extension M/F of algebraic function fields and an iso-dual generalized geometric Goppa code over F, we extend the construction of [CPQT24] to obtain iso- dual generalized geometric Goppa codes over M. Furthermore, we study self-duality of generalized AG codes ([XNL99], [DM03]).
ER  -