Equality and iso-duality of Generalized Geometric Goppa codes
Jyoti Dasgupta, Nupur Patanker
Source 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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