[2303.01721] Block Codes in Pomset Metric over $\mathbb{Z}_m$
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Computer Science > Information Theory

arXiv:2303.01721 (cs)
[Submitted on 3 Mar 2023]

Title:Block Codes in Pomset Metric over $\mathbb{Z}_m$

Authors:W. Ma, J. Luo
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Abstract:In this paper, we introduce codes equipped with pomset block metric. A Singleton type bound for pomset block codes is obtained. Code achieving the Singleton bound, called a maximum distance separable code (for short, MDS ($\mathbb{P},\pi$)-code) is also investigated. We extend the concept of $I$-perfect codes and $r$-perfect codes to pomset block metric. The relation between $I$-perfect codes and MDS $(\mathbb{P},\pi)$-codes is also considered. When all blocks have the same dimension, we prove the duality theorem for codes and study the weight distribution of MDS pomset block codes when the pomset is a chain.
Comments: 26 pages
Subjects: Information Theory (cs.IT)
Cite as: arXiv:2303.01721 [cs.IT]
  (or arXiv:2303.01721v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2303.01721

Submission history

From: Wen Ma [view email]
[v1] Fri, 3 Mar 2023 05:52:10 UTC (18 KB)
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