(1 + u)-Constacyclic codes over Z(4) + uZ(4)

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z(4) + uZ(4) of any length are studied. A new Gray map between Z(4) + uZ(4) and Z(4)(4) is defined. By me...

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Detalles Bibliográficos
Autores principales: Yu, Haifeng, Wang, Yu, Shi, Minjia
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4980856/
https://www.ncbi.nlm.nih.gov/pubmed/27563520
http://dx.doi.org/10.1186/s40064-016-2717-0
Descripción
Sumario:Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z(4) + uZ(4) of any length are studied. A new Gray map between Z(4) + uZ(4) and Z(4)(4) is defined. By means of this map, it is shown that the Z(4) Gray image of a (1 + u)-constacyclic code of length n over Z(4) + uZ(4) is a cyclic code over Z(4) of length 4n. Furthermore, by combining the classical Gray map between Z(4) and F(2)(2), it is shown that the binary image of a (1 + u)-constacyclic code of length n over Z(4) + uZ(4) is a distance invariant binary quasi-cyclic code of index 4 and length 8n. Examples of good binary codes are constructed to illustrate the application of this class of codes.

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