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arXiv · 2609.25740

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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Jyoti Dasgupta, Nupur Patanker. 2026-09-22. Equality and iso-duality of Generalized Geometric Goppa codes. https://arxiv.org/abs/2609.25740

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