Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Codes with Weighted Poset Metrics Based on the Lattice of Subgroups of Z_m

Version 1 : Received: 19 October 2024 / Approved: 20 October 2024 / Online: 21 October 2024 (10:34:17 CEST)

How to cite: Jitjankarn, P. Codes with Weighted Poset Metrics Based on the Lattice of Subgroups of Z_m. Preprints 2024, 2024101556. https://doi.org/10.20944/preprints202410.1556.v1 Jitjankarn, P. Codes with Weighted Poset Metrics Based on the Lattice of Subgroups of Z_m. Preprints 2024, 2024101556. https://doi.org/10.20944/preprints202410.1556.v1

Abstract

By combining a lattice subgroup diagram of Z_m with a weighted poset metric, we introduce a new weighted coordinates poset metric for codes over Z_m , called LS-poset metric. When I is an ideal in a poset, the concept of I-perfect codes with LS-poset metric is investigated. We obtain a Singleton bound for codes with LS-poset metric and define MDS codes. When the poset in poset metric is a chain, we provide sufficient conditions for a code with LS-poset metric to be r-perfect for some r ∈ N .

Keywords

MDS codes; poset codes; pomset codes; perfect codes

Subject

Computer Science and Mathematics, Discrete Mathematics and Combinatorics

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