Generalized Skew Multivariate Goppa Codes

Elena Berardini; Pranav Trivedi

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arXiv · 2605.06580

Generalized Skew Multivariate Goppa Codes

Elena Berardini·Pranav Trivedi

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Abstract

We introduce Generalized Skew Multivariate Goppa codes relying on the theory of multivariate Ore polynomials. These codes contain, as a particular case, the Generalized Skew Goppa codes. By providing a new parity check matrix for the latter, we show that, under some hypotheses, they are subfield subcodes of Generalized Skew Reed--Solomon codes. This result turns out to be helpful to study the parameters of Skew Multivariate Goppa codes, for which we provide bounds on their dimension and minimum distance.

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Elena Berardini, Pranav Trivedi. 2026-05-07. Generalized Skew Multivariate Goppa Codes. https://arxiv.org/abs/2605.06580

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