Abstract

We introduce a block LS-poset (partially ordered set) metric on ℤⁿ<inf>m</inf> constructed from a block decomposition of ℤⁿ<inf>m</inf>, a poset structure on the block indices, and the lattice of subgroups of ℤ<inf>m</inf> arising from the prime factorization of m. Using a multiset representation associated with this subgroup lattice, we define the block LS-poset weight and show that the induced distance is a metric on ℤⁿ<inf>m</inf>. We investigate the geometry of r-balls and I-balls and establish their fundamental properties, including linearity, translation invariance, and duality. These structural results lead to characterizations of I-perfect block LS-poset codes for ideals with full count and partial count. We further derive a Singleton-type bound for block LS-poset codes and introduce the notions of maximum distance separable (MDS) and partial-MDS block LS-poset codes. Connections among perfect codes, MDS codes, and r-perfect codes are also examined for certain classes of posets.