Both linear complementary dual (LCD) codes and maximum distance separable (MDS) codes have good algebraic structures, and they have interesting practical applications such as communication systems, data storage, quantum codes, and so on. So far, most of LCD MDS codes have been constructed by employing generalized Reed-Solomon codes. In this paper we construct some classes of new Euclidean LCD MDS codes and Hermitian LCD MDS codes which are not monomially equivalent to Reed-Solomon codes, called LCD MDS codes of non-Reed-Solomon type. Our method is based on the constructions of Beelen et al. (2017) and Roth and Lempel (1989). To the best of our knowledge, this is the first paper on the construction of LCD MDS codes of non-Reed-Solomon type; any LCD MDS code of non-Reed-Solomon type constructed by our method is not monomially equivalent to any LCD code constructed by the method of Carlet et al. (2018).
Bibliographical noteFunding Information:
Manuscript received June 24, 2020; revised January 22, 2021; accepted May 8, 2021. Date of publication June 7, 2021; date of current version July 14, 2021. The work of Yansheng Wu was supported by the startup fund for talent introduction at the Nanjing University of Posts and Telecommunications (NUPTSF) under Grant NY220137. The work of Jong Yoon Hyun was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government under Grant NRF-2017R1D1A1B05030707. The work of Yoonjin Lee was supported in part by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education under Grant 2019R1A6A1A11051177 and in part by the National Research Foundation of Korea (NRF) grant funded by the Korean Government under Grant NRF-2017R1A2B2004574. (Corresponding author: Jong Yoon Hyun.) Yansheng Wu is with the School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China, and also with the Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China (e-mail: firstname.lastname@example.org).
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- LCD codes
- Linear complementary dual codes
- MDS codes
- Reed-Solomon codes
- non-Reed-Solomon codes