Linear and cyclic codes over direct product of finite chain rings

J. Borges; C. Fernández-Córdoba; R. Ten-Valls

doi:10.1002/mma.4491

Linear and cyclic codes over direct product of finite chain rings

J. Borges, C. Fernández-Córdoba, R. Ten-Valls

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Copyright © 2017 John Wiley & Sons, Ltd. We introduce a new type of linear and cyclic codes. These codes are defined over a direct product of 2 finite chain rings. The definition of these codes as certain submodules of the direct product of copies of these rings is given, and the cyclic property is defined. Cyclic codes can be seen as submodules of the direct product of polynomial rings. Generator matrices for linear codes and generator polynomials for cyclic codes are determined. Further, we study the concept of duality.

Idioma original	Anglès
Pàgines (de-a)	6519-6529
Revista	Mathematical Methods in the Applied Sciences
Volum	41
Número	16
DOIs	https://doi.org/10.1002/mma.4491
Estat de la publicació	Publicada - 15 de nov. 2018

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10.1002/mma.4491

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title = "Linear and cyclic codes over direct product of finite chain rings",

abstract = "Copyright {\textcopyright} 2017 John Wiley & Sons, Ltd. We introduce a new type of linear and cyclic codes. These codes are defined over a direct product of 2 finite chain rings. The definition of these codes as certain submodules of the direct product of copies of these rings is given, and the cyclic property is defined. Cyclic codes can be seen as submodules of the direct product of polynomial rings. Generator matrices for linear codes and generator polynomials for cyclic codes are determined. Further, we study the concept of duality.",

keywords = "codes over rings, cyclic codes, finite chain rings, linear codes",

author = "J. Borges and C. Fern{\'a}ndez-C{\'o}rdoba and R. Ten-Valls",

year = "2018",

month = nov,

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T1 - Linear and cyclic codes over direct product of finite chain rings

AU - Borges, J.

AU - Fernández-Córdoba, C.

AU - Ten-Valls, R.

PY - 2018/11/15

Y1 - 2018/11/15

N2 - Copyright © 2017 John Wiley & Sons, Ltd. We introduce a new type of linear and cyclic codes. These codes are defined over a direct product of 2 finite chain rings. The definition of these codes as certain submodules of the direct product of copies of these rings is given, and the cyclic property is defined. Cyclic codes can be seen as submodules of the direct product of polynomial rings. Generator matrices for linear codes and generator polynomials for cyclic codes are determined. Further, we study the concept of duality.

AB - Copyright © 2017 John Wiley & Sons, Ltd. We introduce a new type of linear and cyclic codes. These codes are defined over a direct product of 2 finite chain rings. The definition of these codes as certain submodules of the direct product of copies of these rings is given, and the cyclic property is defined. Cyclic codes can be seen as submodules of the direct product of polynomial rings. Generator matrices for linear codes and generator polynomials for cyclic codes are determined. Further, we study the concept of duality.

KW - codes over rings

KW - cyclic codes

KW - finite chain rings

KW - linear codes

U2 - 10.1002/mma.4491

DO - 10.1002/mma.4491

M3 - Article

SN - 0170-4214

VL - 41

SP - 6519

EP - 6529

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 16

ER -

Linear and cyclic codes over direct product of finite chain rings

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