A notion of multivariate BCH bounds and codes

In this extended abstract, we use the techniques of computation of the minimum apparent distance of a hypermatrix given in [2] in order to develop a notion of BCH bound and BCH code in the multivariate case. Then we extend the most classical results in BCH codes to the multivariate case and we show how to construct abelian codes with maximum dimension with respect to prefixed bounds for their minimum distance.