Skew Cyclic Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$

• SHI Minjia

  Key Laboratory of Intelligent Computing & Signal Processing Ministry of Education, Anhui University School of Mathematical Sciences, Anhui University

• YAO Ting

  School of Mathematical Sciences, Anhui University

• ALAHMADI Adel

  Department of Mathematics, King Abdulaziz University

• SOLÉ Patrick

  Telecom ParisTech

抄録

In this article, we study skew cyclic codes over $R=\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and v³=v. We describe the generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over R by a decomposition theorem. We also describe the generator polynomial of the dual of a skew cyclic code over R. Moreover, the idempotent generators of skew cyclic codes over $\mathbb{F}_{q}$ and R are considered.

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E98.A (8), 1845-1848, 2015

  一般社団法人 電子情報通信学会

キーワード

• linear codes
• dual codes
• skew cyclic codes
• generator polynomial
• gray map

詳細情報

• CRID: 1390001206310053248
• NII論文ID: 130005089888
• DOI: 10.1587/transfun.e98.a.1845
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E98.A/8/E98.A_1845/_pdf
• 本文言語コード: en
• データソース種別:
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• 抄録ライセンスフラグ: 使用不可