Computing Efficiently a Parity-Check Matrix for Zps-Additive Codes

The Zps-additive codes of length n are subgroups of Znps, with p prime and s ≥ 1 . They can be seen as a generalization of linear codes over Z2, Z4, or more general over Z2s. In this paper, we show two methods for computing a parity-check matrix of a Zps-additive code from a generator matrix of the...

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Detalles Bibliográficos
Autores: Fernández Córdoba, Cristina|||0000-0001-5880-144X, Torres Martín, Adrián|||0000-0002-2489-8930, Vela, Carlos|||0000-0003-3362-8817, Villanueva, M|||0000-0001-6179-0833
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:293051
Acceso en línea:https://ddd.uab.cat/record/293051
https://dx.doi.org/urn:doi:10.1109/TIT.2024.3370410
Access Level:acceso abierto
Palabra clave:Additive code
Chain ring
Parity-check matrix
Performance
Time complexity
Descripción
Sumario:The Zps-additive codes of length n are subgroups of Znps, with p prime and s ≥ 1 . They can be seen as a generalization of linear codes over Z2, Z4, or more general over Z2s. In this paper, we show two methods for computing a parity-check matrix of a Zps-additive code from a generator matrix of the code in standard form. We also compare the performance of our results implemented in Magma with the current available function in Magma for linear codes over finite rings in general. Complementing this comparison, we also show a time complexity analysis of the algorithms. The rings Zps belong to a more general class of rings: finite chain rings. Along the paper, we observe that the same results can be applied to any linear code over a finite commutative chain ring.