One generator quasi-cyclic codes over F 2+uF 2

Irfan Siap; Taher Abualrub; Bahattin Yildiz

doi:10.1016/j.jfranklin.2011.10.020

One generator quasi-cyclic codes over F ₂+uF ₂

Irfan Siap, Taher Abualrub, Bahattin Yildiz

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

18 Scopus citations

Abstract

In this paper, we study quasi-cyclic codes over the ring R=F ₂u+F ₂=0,1,u,u1 where u ²=0. By exploring their structure, we determine the type of one generator quasi-cyclic codes over R and the size by giving a minimal spanning set. We also determine the rank and introduce a lower bound for the minimum distance of free quasi-cyclic codes over R. We include some examples of quasi-cyclic codes of various lengths over R. In particular, we obtain a family of 2-quasi-cyclic codes from cyclic codes over the ring F ₂u+F ₂v+F ₂+uvF ₂. Finally, using the Gray map we obtain a family of optimal binary linear codes as the images of quasi-cyclic codes over R.

Original language	English (US)
Pages (from-to)	284-292
Number of pages	9
Journal	Journal of the Franklin Institute
Volume	349
Issue number	1
DOIs	https://doi.org/10.1016/j.jfranklin.2011.10.020
State	Published - Feb 2012
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.2011.10.020

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title = "One generator quasi-cyclic codes over F 2+uF 2 ",

abstract = "In this paper, we study quasi-cyclic codes over the ring R=F 2u+F 2=0,1,u,u1 where u 2=0. By exploring their structure, we determine the type of one generator quasi-cyclic codes over R and the size by giving a minimal spanning set. We also determine the rank and introduce a lower bound for the minimum distance of free quasi-cyclic codes over R. We include some examples of quasi-cyclic codes of various lengths over R. In particular, we obtain a family of 2-quasi-cyclic codes from cyclic codes over the ring F 2u+F 2v+F 2+uvF 2. Finally, using the Gray map we obtain a family of optimal binary linear codes as the images of quasi-cyclic codes over R.",

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AU - Siap, Irfan

AU - Abualrub, Taher

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N2 - In this paper, we study quasi-cyclic codes over the ring R=F 2u+F 2=0,1,u,u1 where u 2=0. By exploring their structure, we determine the type of one generator quasi-cyclic codes over R and the size by giving a minimal spanning set. We also determine the rank and introduce a lower bound for the minimum distance of free quasi-cyclic codes over R. We include some examples of quasi-cyclic codes of various lengths over R. In particular, we obtain a family of 2-quasi-cyclic codes from cyclic codes over the ring F 2u+F 2v+F 2+uvF 2. Finally, using the Gray map we obtain a family of optimal binary linear codes as the images of quasi-cyclic codes over R.

AB - In this paper, we study quasi-cyclic codes over the ring R=F 2u+F 2=0,1,u,u1 where u 2=0. By exploring their structure, we determine the type of one generator quasi-cyclic codes over R and the size by giving a minimal spanning set. We also determine the rank and introduce a lower bound for the minimum distance of free quasi-cyclic codes over R. We include some examples of quasi-cyclic codes of various lengths over R. In particular, we obtain a family of 2-quasi-cyclic codes from cyclic codes over the ring F 2u+F 2v+F 2+uvF 2. Finally, using the Gray map we obtain a family of optimal binary linear codes as the images of quasi-cyclic codes over R.

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One generator quasi-cyclic codes over F ₂+uF ₂

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