Generalized Skew Multivariate Goppa Codes
Information Theory
2026-05-12 v2 math.IT
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.
Cite
@article{arxiv.2605.06580,
title = {Generalized Skew Multivariate Goppa Codes},
author = {Elena Berardini and Pranav Trivedi},
journal= {arXiv preprint arXiv:2605.06580},
year = {2026}
}
Comments
17 pages