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      New LCD MDS codes of non-Reed-Solomon type

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          Abstract

          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).

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          Author and article information

          Journal
          17 May 2021
          Article
          2105.08263

          http://creativecommons.org/licenses/by/4.0/

          Custom metadata
          9 pages. To appear in IEEE Transactions on Information Theory
          cs.IT math.IT

          Numerical methods, Information systems & theory

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