Block codes on pomset metric

Abstract

Given a regular multiset [Formula: see text] on [Formula: see text], a partial order [Formula: see text] on [Formula: see text], and a label map [Formula: see text] defined by [Formula: see text] with [Formula: see text], we define a pomset block metric [Formula: see text] on the direct sum [Formula: see text] of [Formula: see text] based on the pomset [Formula: see text]. The pomset block metric extends the classical pomset metric introduced by Sudha and Selvaraj and generalizes the poset block metric introduced by Alves et al. over [Formula: see text]. The space [Formula: see text] is called the pomset block space and we determine the complete weight distribution of it. Further, [Formula: see text]-perfect pomset block codes for ideals with partial and full counts are described. Then, for block codes with chain pomset, the packing radius and Singleton bound are established. The relation between maximum distance separable (MDS) codes and [Formula: see text]-perfect codes for any ideal [Formula: see text] is investigated. Moreover, the duality theorem for an MDS pomset block code is established when all the blocks have the same size.