Some new binary quasi-cyclic codes from codes over the ring F2 + u F2 + v F2 + u v F2

Nuh Aydin; Suat Karadeniz; Bahattin Yildiz

doi:10.1007/s00200-013-0207-y

Some new binary quasi-cyclic codes from codes over the ring F₂ + u F₂ + v F₂ + u v F₂

Nuh Aydin, Suat Karadeniz, Bahattin Yildiz

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

13 Scopus citations

Abstract

We consider quasi-cyclic codes over the ring F₂ + u F ₂ + v F₂ + u v F₂, a finite non-chain ring that has been recently studied in coding theory. The Gray images of these codes are shown to be binary quasi-cyclic codes. Using this method we have obtained seventeen new binary quasi-cyclic codes that are new additions to the database of binary quasi-cyclic codes. Moreover, we also obtain a number of binary quasi-cyclic codes with the same parameters as best known binary linear codes that otherwise have more complicated constructions.

Original language	English (US)
Pages (from-to)	355-367
Number of pages	13
Journal	Applicable Algebra in Engineering, Communications and Computing
Volume	24
Issue number	5
DOIs	https://doi.org/10.1007/s00200-013-0207-y
State	Published - Nov 2013
Externally published	Yes

Keywords

Cyclic codes
Gray maps
Lee weight
Quasi-cyclic codes

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

Access to Document

10.1007/s00200-013-0207-y

Cite this

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title = "Some new binary quasi-cyclic codes from codes over the ring F2 + u F2 + v F2 + u v F2",

abstract = "We consider quasi-cyclic codes over the ring F2 + u F 2 + v F2 + u v F2, a finite non-chain ring that has been recently studied in coding theory. The Gray images of these codes are shown to be binary quasi-cyclic codes. Using this method we have obtained seventeen new binary quasi-cyclic codes that are new additions to the database of binary quasi-cyclic codes. Moreover, we also obtain a number of binary quasi-cyclic codes with the same parameters as best known binary linear codes that otherwise have more complicated constructions.",

keywords = "Cyclic codes, Gray maps, Lee weight, Quasi-cyclic codes",

author = "Nuh Aydin and Suat Karadeniz and Bahattin Yildiz",

note = "Funding Information: The first author{\textquoteright}s visit was partially supported by The Scientific and Technological Research Council of Turkey (TUBITAK), Grant Number: 1059B211100236. ",

year = "2013",

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T1 - Some new binary quasi-cyclic codes from codes over the ring F2 + u F2 + v F2 + u v F2

AU - Aydin, Nuh

AU - Karadeniz, Suat

AU - Yildiz, Bahattin

N1 - Funding Information: The first author’s visit was partially supported by The Scientific and Technological Research Council of Turkey (TUBITAK), Grant Number: 1059B211100236.

PY - 2013/11

Y1 - 2013/11

N2 - We consider quasi-cyclic codes over the ring F2 + u F 2 + v F2 + u v F2, a finite non-chain ring that has been recently studied in coding theory. The Gray images of these codes are shown to be binary quasi-cyclic codes. Using this method we have obtained seventeen new binary quasi-cyclic codes that are new additions to the database of binary quasi-cyclic codes. Moreover, we also obtain a number of binary quasi-cyclic codes with the same parameters as best known binary linear codes that otherwise have more complicated constructions.

AB - We consider quasi-cyclic codes over the ring F2 + u F 2 + v F2 + u v F2, a finite non-chain ring that has been recently studied in coding theory. The Gray images of these codes are shown to be binary quasi-cyclic codes. Using this method we have obtained seventeen new binary quasi-cyclic codes that are new additions to the database of binary quasi-cyclic codes. Moreover, we also obtain a number of binary quasi-cyclic codes with the same parameters as best known binary linear codes that otherwise have more complicated constructions.

KW - Cyclic codes

KW - Gray maps

KW - Lee weight

KW - Quasi-cyclic codes

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JO - Applicable Algebra in Engineering, Communications and Computing

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