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Construction of long MDS self-dual codes from short codes
Institution:1. School of Mathematics, Southeast University, Nanjing 210096, China;2. Department of Math, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China;1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong 255091, China;2. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;3. School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Republic of Singapore;1. School of Science and Technology, College of arts and science of Hubei Normal University, Huangshi 435109, Hubei, China;2. School of Science, Hubei University of Technology, Wuhan, Hubei 430068, China
Abstract:In this paper, we propose a mechanism on how to construct long MDS self-dual codes from short ones. These codes are special types of generalized Reed-Solomon (GRS) codes or extended generalized Reed-Solomon codes. The main tool is utilizing additive structure or multiplicative structure on finite fields. By applying this method, more MDS self-dual codes can be constructed.
Keywords:MDS code  Self-dual code  Generalized Reed-Solomon code  Extended generalized Reed-Solomon code
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