We introduce Generalized Skew Multivariate Goppa codes relying on the theory of multivariate Ore polynomials. These codes contain Generalized Skew Goppa codes as a special case. By providing a new parity-check matrix for the latter, we show that they are subfield subcodes of duals of Generalized Skew Reed--Solomon codes, up to the inverse field automorphism. This result is then used to study the parameters of Skew Multivariate Goppa codes, for which we provide bounds on their dimension and minimum distance.

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