Self-dual codes over a family of local rings

被引：0

作者：

Dougherty, Steven T. ^{[1
]}

Fernandez-Cordoba, Cristina ^{[2
]}

Ten-Valls, Roger ^{[2
]}

机构：

[1] Univ Scranton, Dept Math, Scranton, PA 18510 USA

[2] Univ Autonoma Barcelona, Dept Informat & Commun Engn, Bellaterra 08193, Spain

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2021年 / 32卷 / 03期

关键词：

Self-dual codes; Codes over rings; Local rings; CYCLIC CODES;

D O I：

10.1007/s00200-020-00466-4

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We construct an infinite family of commutative rings R-q,R-Delta and we study codes over these rings as well as the structure of the rings. We define a canonical Gray map from R-q,R-Delta to vectors over the residue finite field of q elements and use it to relate codes over R-q,R-Delta to codes over the finite field F-q. Finally, we determine the parameters for when self-dual codes exist and give various constructions for self-dual codes over R-q,R-Delta.

引用

页码：265 / 281

页数：17

共 12 条

[1]

Cengellenmis Y., 2012, P ACCT 2012

[2] Codes over an infinite family of rings with a Gray map [J].

Cengellenmis, Yasemin ;

Dertli, Abdullah ;

Dougherty, S. T. .

DESIGNS CODES AND CRYPTOGRAPHY, 2014, 72 (03) :559-580

[3]

Dertli A, 2017, J SCI ARTS, P215

[4]

Dertli A, 2016, J SCI ARTS, P13

[5]

Dertli A, 2016, EUR J PURE APPL MATH, V9, P305

[6]

Dougherty ST, 2017, SPRINGERBRIEF MATH, P1, DOI 10.1007/978-3-319-59806-2

[7] Group rings, G-codes and constructions of self-dual and formally self-dual codes [J].

Dougherty, Steven T. ;

Gildea, Joseph ;

Taylor, Rhian ;

Tylyshchak, Alexander .

DESIGNS CODES AND CRYPTOGRAPHY, 2018, 86 (09) :2115-2138

[8] Quasi-cyclic codes as cyclic codes over a family of local rings [J].

Dougherty, Steven T. ;

Fernandez-Cordoba, Cristina ;

Ten-Valls, Roger .

FINITE FIELDS AND THEIR APPLICATIONS, 2016, 40 :138-149

[9] Foundations of Algebraic Coding Theory [J].

Dougherty, Steven T. .

NONCOMMUTATIVE RINGS AND THEIR APPLICATIONS, 2015, 634 :101-136

[10] Cyclic codes over Rk [J].

Dougherty, Steven T. ;

Karadeniz, Suat ;

Yildiz, Bahattin .

DESIGNS CODES AND CRYPTOGRAPHY, 2012, 63 (01) :113-126

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