Block Codes on Pomset Metric
Atul Kumar Shriwastva, R. S. Selvaraj

TL;DR
This paper introduces a new class of block codes based on pomset metrics, extending existing poset and pomset metrics, and explores their weight distribution, perfect codes, bounds, and duality properties.
Contribution
It defines the pomset block metric on direct sums of modules, generalizes previous metrics, and studies code properties like perfectness, bounds, and duality within this framework.
Findings
Complete weight distribution of pomset block space determined.
Characterization of $I$-perfect pomset block codes provided.
Established bounds and duality theorems for MDS pomset block codes.
Abstract
Given a regular multiset on , a partial order on , and a label map defined by with , we define a pomset block metric on the direct sum of based on the pomset . The pomset block metric extends the classical pomset metric introduced by I. G. Sudha and R. S. Selvaraj and generalizes the poset block metric introduced by M. M. S. Alves et al over . The space is called the pomset block space and we determine the complete weight distribution of it. Further, -perfect pomset block codes for ideals with partial and full counts are described. Then, for block codes with chain pomset, the…
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Rings, Modules, and Algebras
