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Explicit MDS Codes With Complementary Duals

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In 1964, Massey introduced a class of codes with complementary duals which are called linear complimentary dual (LCD) codes. He showed that LCD codes have applications in communication system, side-channel… Click to show full abstract

In 1964, Massey introduced a class of codes with complementary duals which are called linear complimentary dual (LCD) codes. He showed that LCD codes have applications in communication system, side-channel attack and so on. LCD codes have been extensively studied in literature. On the other hand, MDS codes form an optimal family of classical codes which have wide applications in both theory and practice. The main purpose of this paper is to give an explicit construction of several classes of LCD MDS codes, using tools from algebraic function fields. We exemplify this construction and obtain several classes of explicit LCD MDS codes for the odd characteristic case.

Keywords: mds codes; lcd codes; codes complementary; explicit mds; complementary duals

Journal Title: IEEE Transactions on Information Theory
Year Published: 2018

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