Linear, Cyclic and constacyclic codes over S4 = F2 + uF2 + u2F2 + u3F2

Zeynep ÖDemiş Özger; ÜMmü ÜMare Kara; Bahattin Yıldız

doi:10.2298/FIL1405897O

Linear, Cyclic and constacyclic codes over S₄ = F₂ + uF₂ + u²F₂ + u³F₂

Zeynep ÖDemiş Özger, ÜMmü ÜMare Kara, Bahattin Yıldız

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

7 Scopus citations

Abstract

In this work, linear codes over the ring S₄ = F₂ + uF₂ + u²F₂ + u³F₂ are considered. The Lee weight and gray map for codes over S4 are defined and MacWilliams identities for the complete, the symmetrized and the Lee weight enumerators are obtained. Cyclic and (1 + u²)-constacyclic codes over S4 are studied, as a result of which a substantial number of optimal binary codes of different lengths are obtained as the Gray images of cyclic and constacyclic codes over S₄.

Original language	English (US)
Pages (from-to)	897-906
Number of pages	10
Journal	Filomat
Volume	28
Issue number	5
DOIs	https://doi.org/10.2298/FIL1405897O
State	Published - 2014
Externally published	Yes

Keywords

Constacyclic Codes
Cyclic Codes
Finite Chain Rings
Negacyclic Codes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.2298/FIL1405897O

Cite this

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title = "Linear, Cyclic and constacyclic codes over S4 = F2 + uF2 + u2F2 + u3F2",

abstract = "In this work, linear codes over the ring S4 = F2 + uF2 + u2F2 + u3F2 are considered. The Lee weight and gray map for codes over S4 are defined and MacWilliams identities for the complete, the symmetrized and the Lee weight enumerators are obtained. Cyclic and (1 + u2)-constacyclic codes over S4 are studied, as a result of which a substantial number of optimal binary codes of different lengths are obtained as the Gray images of cyclic and constacyclic codes over S4.",

keywords = "Constacyclic Codes, Cyclic Codes, Finite Chain Rings, Negacyclic Codes",

author = "{\"O}zger, {Zeynep {\"O}Demi{\c s}} and Kara, {{\"U}Mm{\"u} {\"U}Mare} and Bahattin Yıldız",

year = "2014",

doi = "10.2298/FIL1405897O",

language = "English (US)",

volume = "28",

pages = "897--906",

journal = "Filomat",

issn = "0354-5180",

publisher = "Universitet of Nis",

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TY - JOUR

T1 - Linear, Cyclic and constacyclic codes over S4 = F2 + uF2 + u2F2 + u3F2

AU - Özger, Zeynep ÖDemiş

AU - Kara, ÜMmü ÜMare

AU - Yıldız, Bahattin

PY - 2014

Y1 - 2014

N2 - In this work, linear codes over the ring S4 = F2 + uF2 + u2F2 + u3F2 are considered. The Lee weight and gray map for codes over S4 are defined and MacWilliams identities for the complete, the symmetrized and the Lee weight enumerators are obtained. Cyclic and (1 + u2)-constacyclic codes over S4 are studied, as a result of which a substantial number of optimal binary codes of different lengths are obtained as the Gray images of cyclic and constacyclic codes over S4.

AB - In this work, linear codes over the ring S4 = F2 + uF2 + u2F2 + u3F2 are considered. The Lee weight and gray map for codes over S4 are defined and MacWilliams identities for the complete, the symmetrized and the Lee weight enumerators are obtained. Cyclic and (1 + u2)-constacyclic codes over S4 are studied, as a result of which a substantial number of optimal binary codes of different lengths are obtained as the Gray images of cyclic and constacyclic codes over S4.

KW - Constacyclic Codes

KW - Cyclic Codes

KW - Finite Chain Rings

KW - Negacyclic Codes

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U2 - 10.2298/FIL1405897O

DO - 10.2298/FIL1405897O

M3 - Article

SN - 0354-5180

VL - 28

SP - 897

EP - 906

JO - Filomat

JF - Filomat

IS - 5

ER -