Generalized Skew Multivariate Goppa Codes
Elena Berardini, Pranav Trivedi
TL;DR
This paper introduces a new class of multivariate Goppa codes based on Ore polynomials, providing new parity check matrices and analyzing their parameters and subfield subcode relationships.
Contribution
It extends skew Goppa codes to multivariate cases using Ore polynomial theory and offers new bounds on their parameters.
Findings
New parity check matrix for generalized skew Goppa codes
Codes are subfield subcodes of skew Reed--Solomon codes under certain conditions
Provides bounds on dimension and minimum distance of these codes
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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