Polycyclic codes as invariant subspaces |
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| Institution: | 1. Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China;2. School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China;3. School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran;4. I2M, (CNRS, University of Aix-Marseille, Centrale Marseille), Marseilles, France;1. Institute of Analysis and Number Theory, Graz University of Technology, Kopernikusgasse 24/II, A-8010 Graz, Austria;2. School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland;3. School of Mathematics, Wits University, Johannesburg, South Africa;4. Research Group in Algebraic Structures and Applications, King Abdulaziz University, Jeddah, Saudi Arabia;5. Centro de Ciencias Matemáticas, UNAM, Morelia, Mexico;1. Faculty of Mathematics, University of Science and Technology Houari Boumediene, Algeria;2. Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, Spain;3. Department of Mathematics, University of Scranton, United States of America;1. Math Department, King Abdulaziz University, Jeddah, Saudi Arabia;2. Dép. de Mathématique, Université d’Artois, Lens, France;3. Telecom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France |
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| Abstract: | Polycyclic codes are a powerful generalization of cyclic and constacyclic codes. Their algebraic structure is studied here by the theory of invariant subspaces from linear algebra. As an application, a bound on the minimum distance of these codes is derived which outperforms, in some cases, the natural analogue of the BCH bound. |
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| Keywords: | Polycyclic codes Cyclic codes BCH bound Invariant subspaces |
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