Weighted Coordinates Poset Block Codes
Atul Kumar Shriwastva, R. S. Selvaraj

TL;DR
This paper introduces a generalized weighted coordinates poset block metric for coding theory, extending previous metrics and deriving key properties like weight distribution and bounds.
Contribution
It defines the weighted coordinates poset block metric, generalizes existing metrics, and determines the complete weight distribution and bounds for codes under this new metric.
Findings
Derived the complete weight distribution of the $(P,w, ext{pi})$-space.
Established the Singleton bound for $(P,w, ext{pi})$-codes.
Re-obtained the Singleton bound for $(P, ext{pi})$-metric and $P$-metric.
Abstract
Given , a partial order on , a label map defined by with , the direct sum of , and a weight function on , we define a poset block metric on based on the poset . The metric is said to be weighted coordinates poset block metric (-metric). It extends the weighted coordinates poset metric (-metric) introduced by L. Panek and J. A. Pinheiro and generalizes the poset block metric (-metric) introduced by M. M. S. Alves et al. We determine the complete weight distribution of a -space, thereby obtaining it for -space, -space,…
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research
