Weighted coordinates poset block codes

This paper defines a new metric called weighted coordinates poset block metric [Formula: see text]-metric). This metric generalizes the weighted coordinates poset metric ([Formula: see text]-metric) introduced by Panek and Pinheiro, and the poset block metric ([Formula: see text]-metric) defined by Alves et al. A Singleton bound for [Formula: see text]-metric codes is derived and [Formula: see text]-MDS codes are defined. An upper and a lower bound on the minimum distance of [Formula: see text]-MDS codes are also derived when all the blocks have the same size. Relations among minimum distances of codes in [Formula: see text]-space, [Formula: see text]-space, [Formula: see text]-space, [Formula: see text]-space and [Formula: see text]-space are arrived at. In addition, when [Formula: see text] is a chain, the relation between packing radius and minimum distance of an NRT [Formula: see text]-code is derived. Moreover, characterizations of NRT [Formula: see text] MDS codes are established, which led to the duality theorem, when all the blocks have the same size. Finally, when [Formula: see text] is a hierarchical poset, we study the [Formula: see text]-ball, weight-distribution of [Formula: see text]-space, minimum distance and packing radius of a [Formula: see text]-code.