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...
| Autores: | , , , |
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| 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 |
| 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. |
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