On ZprZps-additive cyclic codes

Joaquim Borges; Cristina Fernández-Córdoba; Roger Ten-Valls

doi:10.3934/amc.2018011

On ZprZps-additive cyclic codes

Joaquim Borges, Cristina Fernández-Córdoba, Roger Ten-Valls

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Resum

© 2018 AIMS. A Zpr Zps -additive code, r ≤ s, is a Zps-submodule of (Formula presented) We introduce Zpr Zps -additive cyclic codes. These codes can be seen as (Formula presented)- submodules of (Formula presented). We determine the generator polynomials of a code over (Formula presented) and a minimal spanning set over (Formula presented) in terms of the generator polynomials. We also study the duality in the module (Formula presented). Our results generalise those for Z2Z4 -additive cyclic codes.

Idioma original	Anglès
Pàgines (de-a)	169-179
Revista	Advances in Mathematics of Communications
Volum	12
Número	1
DOIs	https://doi.org/10.3934/amc.2018011
Estat de la publicació	Publicada - 1 de febr. 2018

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10.3934/amc.2018011

https://ddd.uab.cat/record/188178

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title = "On ZprZps-additive cyclic codes",

abstract = "{\textcopyright} 2018 AIMS. A Zpr Zps -additive code, r ≤ s, is a Zps-submodule of (Formula presented) We introduce Zpr Zps -additive cyclic codes. These codes can be seen as (Formula presented)- submodules of (Formula presented). We determine the generator polynomials of a code over (Formula presented) and a minimal spanning set over (Formula presented) in terms of the generator polynomials. We also study the duality in the module (Formula presented). Our results generalise those for Z2Z4 -additive cyclic codes.",

keywords = "Additive codes, Codes over rings, Cyclic codes, Duality",

author = "Joaquim Borges and Cristina Fern{\'a}ndez-C{\'o}rdoba and Roger Ten-Valls",

year = "2018",

month = feb,

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doi = "10.3934/amc.2018011",

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TY - JOUR

T1 - On ZprZps-additive cyclic codes

AU - Borges, Joaquim

AU - Fernández-Córdoba, Cristina

AU - Ten-Valls, Roger

PY - 2018/2/1

Y1 - 2018/2/1

N2 - © 2018 AIMS. A Zpr Zps -additive code, r ≤ s, is a Zps-submodule of (Formula presented) We introduce Zpr Zps -additive cyclic codes. These codes can be seen as (Formula presented)- submodules of (Formula presented). We determine the generator polynomials of a code over (Formula presented) and a minimal spanning set over (Formula presented) in terms of the generator polynomials. We also study the duality in the module (Formula presented). Our results generalise those for Z2Z4 -additive cyclic codes.

AB - © 2018 AIMS. A Zpr Zps -additive code, r ≤ s, is a Zps-submodule of (Formula presented) We introduce Zpr Zps -additive cyclic codes. These codes can be seen as (Formula presented)- submodules of (Formula presented). We determine the generator polynomials of a code over (Formula presented) and a minimal spanning set over (Formula presented) in terms of the generator polynomials. We also study the duality in the module (Formula presented). Our results generalise those for Z2Z4 -additive cyclic codes.

KW - Additive codes

KW - Codes over rings

KW - Cyclic codes

KW - Duality

U2 - 10.3934/amc.2018011

DO - 10.3934/amc.2018011

M3 - Article

SN - 1930-5346

VL - 12

SP - 169

EP - 179

JO - Advances in Mathematics of Communications

JF - Advances in Mathematics of Communications

IS - 1

ER -

On ZprZps-additive cyclic codes

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