Constructions of self-dual codes and formally self-dual codes over rings

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• 作者：Steven T Dougherty ; Abidin Kaya…
• 关键词：Self ; dual codes ; Formally self ; dual codes ; Codes over rings
• 刊名：Applicable Algebra in Engineering, Communication and Computing
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：27
• 期：5
• 页码：435-449
• 全文大小：421 KB
• 刊物类别：Computer Science
• 刊物主题：Symbolic and Algebraic Manipulation
  Computer Hardware
  Theory of Computation
  Artificial Intelligence and Robotics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0622
• 卷排序：27

文摘

We shall describe several families of X-rings and construct self-dual and formally self-dual codes over these rings. We then use a Gray map to construct binary formally self-dual codes from these codes. In several cases, we produce binary formally self-dual codes with larger minimum distances than known self-dual codes. We also produce non-linear codes which are better than the best known linear codes.