Generalized Skew Multivariate Goppa Codes
This work advances coding theory by generalizing existing code families, but the results are theoretical and incremental, with no concrete performance numbers or practical applications demonstrated.
The paper introduces Generalized Skew Multivariate Goppa codes based on multivariate Ore polynomials, which include Generalized Skew Goppa codes as a special case. It provides a new parity check matrix and shows that under certain hypotheses, these codes are subfield subcodes of Generalized Skew Reed-Solomon codes, yielding bounds on dimension and minimum distance.
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.