Generalized Skew Multivariate Goppa Codes

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.