Extended Abstract: Codes as Modules over Skew Polynomial Rings

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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：83-86
• 全文大小：136 KB
• 参考文献：1.Abualrub, T., Aydin, N., Seneviratne, P.: On R-cyclic codes over F2--em class="EmphasisTypeItalic">vF2. Australas. J. Combin.?54, 115-26 (2012)MATH MathSciNet
  2.Boucher, D., Solé, P., Ulmer, F.: Skew constacyclic codes over galois rings. Advances in Mathematics of Communications?2, 273-92 (2008)View Article MATH MathSciNet
  3.Boucher, D., Ulmer, F.: Codes as modules over skew polynomial rings. In: Parker, M.G. (ed.) Cryptography and Coding 2009. LNCS, vol.?5921, pp. 38-5. Springer, Heidelberg (2009)View Article
  4.Boucher, D., Ulmer, F.: A note on the dual codes of module skew codes. In: Chen, L. (ed.) IMACC 2011. LNCS, vol.?7089, pp. 230-43. Springer, Heidelberg (2011)View Article
  5.Boucher, D., Ulmer, F.: Self-dual skew codes and factorization of skew polynomials. Journal of Symbolic Computation?60, 47-1 (2014)View Article MATH MathSciNet
  6.Bhaintwal, M.: Skew quasi-cyclic codes over Galois rings, Des. Codes Cryptogr.?62, 85-01 (2012)View Article MATH MathSciNet
  7.Szabo, S., Ulmer, F.: Dualilty Preserving Gray Maps (Pseudo) Self-dual Bases and Symmetric Base (preprint) (2015)
  8.Yildiz, B., Karadeniz, S.: Linear codes over F2--em class="EmphasisTypeItalic">uF2--em class="EmphasisTypeItalic">vF2--em class="EmphasisTypeItalic">uvF2. Des. Codes Cryptogr.?54(1), 61-1 (2010)View Article MATH MathSciNet
  
• 作者单位：Felix Ulmer (17)
  
  17. IRMAR, CNRS, UMR 6625, Université de Rennes 1, Université Européenne de Bretagne, Rennes Cedex, 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

This talk is an overview of codes that are defined as modules over skew polynomial rings. These codes can be seen as a generalization of cyclic codes or more generally polynominal codes to a non commutative polynomial ring. Most properties of classical cyclic codes can be generalized to this new setting and self-dual codes can be easily identified. Those rings are no longer unique factorization rings, therefore there are many factors of X n ??-, each generating a “skew cyclic code- In previous works many new codes and new self-dual codes with a better distance than existing codes have been found. Recently cyclic and skew-cyclic codes over rings have been extensively studied in order to obtain codes over subfields (or subrings) under mapping with good properties.