Construction of skew cyclic codes over $\mathbb F_q+v\mathbb F_q$

Fatmanur Gursoy; Irfan Siap; Bahattin Yildiz

doi:10.3934/amc.2014.8.313

Article Contents

2014, Volume 8, Issue 3: 313-322. Doi: 10.3934/amc.2014.8.313

This issue Previous Article Linear complexity of cyclotomic sequences of order six and BCH codes over GF(3) Next Article How to obtain division algebras used for fast-decodable space-time block codes

Construction of skew cyclic codes over $\mathbb F_q+v\mathbb F_q$

1.
Department of Mathematics, Yildiz Technical University, 34210, Istanbul
2.
Department of Mathematics, Fatih University, 34500, Istanbul

Received: April 30, 2013

Revised: June 30, 2013

Published: July 2014

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Abstract

In this paper skew cyclic codes over the the family of rings $\mathbb{F}_q+v\mathbb{F}_q$ with $v^2=v$ are studied for the first time in its generality. Structural properties of skew cyclic codes over $\mathbb{F}_q+v\mathbb{F}_q$ are investigated through a decomposition theorem. It is shown that skew cyclic codes over this ring are principally generated. The idempotent generators of skew-cyclic codes over $\mathbb{F}_q$ and $\mathbb{F}_q+v\mathbb{F}_q$ have been considered for the first time in literature. Moreover, a BCH type bound is presented for the parameters of these codes.

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Mathematics Subject Classification: Primary: 94B15, 94B05; Secondary: 94B99.

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