A Note on the Existence of Self-Dual Skew Codes over Finite Fields

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• 刊名：Lecture Notes in Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：9084
• 期：1
• 页码：228-239
• 全文大小：259 KB
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• 作者单位：Delphine Boucher (17)
  
  17. IRMAR, CNRS, Université de Rennes 1, UMR 6625, Université européenne de Bretagne, 5 Bd Lannec, 35 000, Rennes, France
  
• 丛书名：Codes, Cryptology, and Information Security
• ISBN：978-3-319-18681-8
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

Conditions on the existence of self-dual θ-codes defined over a finite field \({\rm I\!F}_q\) are studied for θ automorphism of \({\rm I\!F}_q\). When \(q \equiv 1 \pmod{4}\) it is proven that there always exists a self-dual θ-code in any dimension and that self-dual θ-codes of a given dimension are either all θ-cyclic or all θ-negacyclic. When \(q \equiv 3 \pmod{4}\), there does not exist a self-dual θ-cyclic code and a necessary and sufficient condition for the existence of self-dual θ-negacyclic codes is given.