Cyclic codes over Rk

Steven T. Dougherty; Suat Karadeniz; Bahattin Yildiz

doi:10.1007/s10623-011-9539-4

Cyclic codes over R_k

Steven T. Dougherty, Suat Karadeniz, Bahattin Yildiz

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

Cyclic codes over an infinite family of rings are defined. The general properties of cyclic codes over these rings are studied, in particular nontrivial one-generator cyclic codes are characterized. It is also proved that the binary images of cyclic codes over these rings under the natural Gray map are binary quasi-cyclic codes of index 2^k . Further, several optimal or near optimal binary codes are obtained from cyclic codes over R_k via this map.

Original language	English (US)
Pages (from-to)	113-126
Number of pages	14
Journal	Designs, Codes, and Cryptography
Volume	63
Issue number	1
DOIs	https://doi.org/10.1007/s10623-011-9539-4
State	Published - Apr 2012
Externally published	Yes

Keywords

Cyclic codes
Gray map
Optimal codes

ASJC Scopus subject areas

Computer Science Applications
Applied Mathematics

Access to Document

10.1007/s10623-011-9539-4

Cite this

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abstract = "Cyclic codes over an infinite family of rings are defined. The general properties of cyclic codes over these rings are studied, in particular nontrivial one-generator cyclic codes are characterized. It is also proved that the binary images of cyclic codes over these rings under the natural Gray map are binary quasi-cyclic codes of index 2k . Further, several optimal or near optimal binary codes are obtained from cyclic codes over Rk via this map.",

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AU - Yildiz, Bahattin

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N2 - Cyclic codes over an infinite family of rings are defined. The general properties of cyclic codes over these rings are studied, in particular nontrivial one-generator cyclic codes are characterized. It is also proved that the binary images of cyclic codes over these rings under the natural Gray map are binary quasi-cyclic codes of index 2k . Further, several optimal or near optimal binary codes are obtained from cyclic codes over Rk via this map.

AB - Cyclic codes over an infinite family of rings are defined. The general properties of cyclic codes over these rings are studied, in particular nontrivial one-generator cyclic codes are characterized. It is also proved that the binary images of cyclic codes over these rings under the natural Gray map are binary quasi-cyclic codes of index 2k . Further, several optimal or near optimal binary codes are obtained from cyclic codes over Rk via this map.

KW - Cyclic codes

KW - Gray map

KW - Optimal codes

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