On LCD, self dual and isodual cyclic codes over finite chain rings

In this paper, LCD cyclic, self dual and isodual codes over finite chain rings are investigated. It was proven recently that a non-free LCD cyclic code does not exist over finite chain rings. Based on algebraic number theory, we introduce necessary and sufficient conditions for which all free cyclic...

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Detalles Bibliográficos
Autores: Benyettou, Amel, Batoul, Aicha, Fernández Córdoba, Cristina|||0000-0001-5880-144X
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:251401
Acceso en línea:https://ddd.uab.cat/record/251401
https://dx.doi.org/urn:doi:10.1016/j.ffa.2022.101993
Access Level:acceso abierto
Palabra clave:LCD
Isodual
Self dual
Cyclic codes
Finite chain rings
Descripción
Sumario:In this paper, LCD cyclic, self dual and isodual codes over finite chain rings are investigated. It was proven recently that a non-free LCD cyclic code does not exist over finite chain rings. Based on algebraic number theory, we introduce necessary and sufficient conditions for which all free cyclic codes over a finite chain ring are LCD. We have also obtained conditions on the existence of non trivial self dual cyclic codes of any length when the nilpotency index of the maximal ideal of a finite chain ring is even. Further, several constructions of isodual codes are given based on the factorization of the polynomial x-1 over a finite chain ring.