@article{Rungratgasame2026, 
author = {Thitarie Rungratgasame and Phichet Jitjankarn},
title = {Block    L  S–poset codes over                      Z              m    n  : Perfect codes, Singleton bound, and MDS characterization},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {14735-14756},
keywords = {block LS–poset metric, poset block code, perfect code, r-perfect code, I-perfect code, MDS code, partial-MDS code, Singleton bound, subgroup lattice, multiset},
url = {https://www.sciopen.com/article/10.3934/math.2026605},
doi = {10.3934/math.2026605},
abstract = {We introduce a block    L  S–poset (partially ordered set) metric on                      Z              m    n   constructed from a block decomposition of                      Z              m    n  , a poset structure on the block indices, and the lattice of subgroups of                      Z              m   arising from the prime factorization of    m. Using a multiset representation associated with this subgroup lattice, we define the block    L  S–poset weight and show that the induced distance is a metric on                      Z              m    n  . 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    L  S–poset codes for ideals with full count and partial count. We further derive a Singleton-type bound for block    L  S–poset codes and introduce the notions of maximum distance separable (MDS) and partial-MDS block    L  S–poset codes. Connections among perfect codes, MDS codes, and    r-perfect codes are also examined for certain classes of posets.}
}