MDS and I-perfect codes in pomset block spaces

In this paper, we establish the Singleton bound for pomset block codes ([Formula: see text]-codes) of length [Formula: see text] over the ring [Formula: see text]. An upper and a lower bound on the minimum distance of [Formula: see text]-Maximum distance separable (MDS) codes are derived. Moreover, we prove that an MDS [Formula: see text]-code is necessarily an MDS [Formula: see text]-code. We also investigate the relationship between the [Formula: see text]-perfect codes and [Formula: see text]-perfect codes. Given an ideal with partial count and full count, we investigate how MDS and [Formula: see text]-perfect codes relate to one another. Duality theorem is derived for an MDS [Formula: see text]-code when all the blocks are of same length, and the distribution of codewords among [Formula: see text]-balls is analyzed as well. Finally, for a chain pomset, we study the maximum distance separability, packing radius and minimum distance of pomset block codes.