Cyclic codes over F2+uF2+vF2+uvF 2

Bahattin Yildiz; Suat Karadeniz

doi:10.1007/s10623-010-9399-3

Cyclic codes over F₂+uF₂+vF₂+uvF ₂

Bahattin Yildiz, Suat Karadeniz

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

69 Scopus citations

Abstract

In this work, we focus on cyclic codes over the ring F₂+uF ₂+vF₂+uvF₂, which is not a finite chain ring. We use ideas from group rings and works of AbuAlrub et.al. in (Des Codes Crypt 42:273-287, 2007) to characterize the ring (F₂+uF₂+vF ₂+uvF₂)/(xⁿ-1) and cyclic codes of odd length. Some good binary codes are obtained as the images of cyclic codes over F ₂+uF₂+vF₂+uvF₂ under two Gray maps that are defined. We also characterize the binary images of cyclic codes over F₂+uF₂+vF₂+uvF₂ in general.

Original language	English (US)
Pages (from-to)	221-234
Number of pages	14
Journal	Designs, Codes, and Cryptography
Volume	58
Issue number	3
DOIs	https://doi.org/10.1007/s10623-010-9399-3
State	Published - Mar 2011
Externally published	Yes

Keywords

Cyclic codes
Gray maps
Homogeneous weight
Lee weight
Quasi-cyclic codes

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science Applications
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1007/s10623-010-9399-3

Cite this

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abstract = "In this work, we focus on cyclic codes over the ring F2+uF 2+vF2+uvF2, which is not a finite chain ring. We use ideas from group rings and works of AbuAlrub et.al. in (Des Codes Crypt 42:273-287, 2007) to characterize the ring (F2+uF2+vF 2+uvF2)/(xn-1) and cyclic codes of odd length. Some good binary codes are obtained as the images of cyclic codes over F 2+uF2+vF2+uvF2 under two Gray maps that are defined. We also characterize the binary images of cyclic codes over F2+uF2+vF2+uvF2 in general.",

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AB - In this work, we focus on cyclic codes over the ring F2+uF 2+vF2+uvF2, which is not a finite chain ring. We use ideas from group rings and works of AbuAlrub et.al. in (Des Codes Crypt 42:273-287, 2007) to characterize the ring (F2+uF2+vF 2+uvF2)/(xn-1) and cyclic codes of odd length. Some good binary codes are obtained as the images of cyclic codes over F 2+uF2+vF2+uvF2 under two Gray maps that are defined. We also characterize the binary images of cyclic codes over F2+uF2+vF2+uvF2 in general.

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KW - Quasi-cyclic codes

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