(1v)-Constacyclic codes over F 2 uF 2 vF 2 uvF 2

Suat Karadeniz; Bahattin Yildiz

doi:10.1016/j.jfranklin.2011.08.005

(1v)-Constacyclic codes over ^{F 2} u^{F 2} v^{F 2} uv^{F 2}

Suat Karadeniz, Bahattin Yildiz

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

34 Scopus citations

Abstract

In this work, (1v)-constacyclic codes over the ring ^F2u ^F2v^F2uv^F2 are studied. (1v)-constacyclic codes over ^F2u^F2v^F2uv^F2 of odd lengths are characterized with the help of cyclic codes over ^F2u ^F2v^F2uv^F2. A natural Gray map from ( ^F2u^F2v^F2uv^F2)ⁿ to ( ^F2u^F2)²ⁿ is introduced and it is shown that the image under this map of (1v)-constacyclic codes over ^F2u ^F2v^F2uv^F2 are cyclic codes over ^F2u^F2. Also a substantial number of optimal binary linear codes are obtained as the images of (1v)-constacyclic codes over ^F2u^F2v^F2uv^F2.

Original language	English (US)
Pages (from-to)	2625-2632
Number of pages	8
Journal	Journal of the Franklin Institute
Volume	348
Issue number	9
DOIs	https://doi.org/10.1016/j.jfranklin.2011.08.005
State	Published - Nov 2011
Externally published	Yes

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications
Applied Mathematics

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10.1016/j.jfranklin.2011.08.005

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title = "(1v)-Constacyclic codes over F 2 uF 2 vF 2 uvF 2",

abstract = "In this work, (1v)-constacyclic codes over the ring F2u F2vF2uvF2 are studied. (1v)-constacyclic codes over F2uF2vF2uvF2 of odd lengths are characterized with the help of cyclic codes over F2u F2vF2uvF2. A natural Gray map from ( F2uF2vF2uvF2)n to ( F2uF2)2n is introduced and it is shown that the image under this map of (1v)-constacyclic codes over F2u F2vF2uvF2 are cyclic codes over F2uF2. Also a substantial number of optimal binary linear codes are obtained as the images of (1v)-constacyclic codes over F2uF2vF2uvF2.",

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AU - Karadeniz, Suat

AU - Yildiz, Bahattin

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N2 - In this work, (1v)-constacyclic codes over the ring F2u F2vF2uvF2 are studied. (1v)-constacyclic codes over F2uF2vF2uvF2 of odd lengths are characterized with the help of cyclic codes over F2u F2vF2uvF2. A natural Gray map from ( F2uF2vF2uvF2)n to ( F2uF2)2n is introduced and it is shown that the image under this map of (1v)-constacyclic codes over F2u F2vF2uvF2 are cyclic codes over F2uF2. Also a substantial number of optimal binary linear codes are obtained as the images of (1v)-constacyclic codes over F2uF2vF2uvF2.

AB - In this work, (1v)-constacyclic codes over the ring F2u F2vF2uvF2 are studied. (1v)-constacyclic codes over F2uF2vF2uvF2 of odd lengths are characterized with the help of cyclic codes over F2u F2vF2uvF2. A natural Gray map from ( F2uF2vF2uvF2)n to ( F2uF2)2n is introduced and it is shown that the image under this map of (1v)-constacyclic codes over F2u F2vF2uvF2 are cyclic codes over F2uF2. Also a substantial number of optimal binary linear codes are obtained as the images of (1v)-constacyclic codes over F2uF2vF2uvF2.

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(1v)-Constacyclic codes over ^{F 2} u^{F 2} v^{F 2} uv^{F 2}

Abstract

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