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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.56 no.1 Bogotá jan./jun. 2022 Epub 02-Fev-2024
https://doi.org/10.15446/recolma.v56n1.105620
Original article
On quantum codes from codes over R m
Sobre códigos cuánticos a través de códigos sobre R m
1 Malayer University, Malayer, Iran
Let R m = Fq[y]/<y m - 1>, where m | q - 1. In this paper, we obtain the structure of linear and cyclic codes over R m . Also, we introduce a preserving-orthogonality Gray map from R m to F m q . Among the main results, we obtain the exact structure of self-orthogonal cyclic codes over R m to introduce parameters of quantum codes from cyclic codes over R m .
Keywords: Self-orthogonal codes; Cyclic codes; Quantum codes
Sea R m = Fq[y]/<y m - 1> donde m | q - 1. En este artículo, obtenemos la estructura de códigos lineales y cíclicos sobre R m . También introducimos una aplicación de Gray de R m a F m q que preserva la ortogonalidad. Entre los resultados principales, obtenemos la estructura exacta de los códigos cíclicos auto-ortogonales sobre R m para introducir parámetros de los códigos cuánticos a través de los códigos cíclicos sobre R m .
Palabras clave: códigos auto-ortogonales; códigos cíclicos; códigos cuánticos
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Received: May 08, 2021; Accepted: May 27, 2022
This is an open-access article distributed under the terms of the Creative Commons Attribution License
