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. Preprints2024, 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
Jitjankarn, P. Codes with Weighted Poset Metrics Based on the Lattice of Subgroups of Z_m. Preprints2024, 2024101556. https://doi.org/10.20944/preprints202410.1556.v1
APA Style
Jitjankarn, P. (2024). Codes with Weighted Poset Metrics Based on the Lattice of Subgroups of Z_m. Preprints. https://doi.org/10.20944/preprints202410.1556.v1
Chicago/Turabian Style
Jitjankarn, P. 2024 "Codes with Weighted Poset Metrics Based on the Lattice of Subgroups of Z_m" Preprints. 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 .
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
