Linear complementary dual, maximum distance separable codes

01/14/2019

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by   Ted Hurley, et al.

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Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given n and r<n, with n or r (or both) odd, MDS LCD (n,r) codes are constructed over finite fields whose characteristic does not divide n. Series of LCD MDS codes are constructed to required rate and required error-correcting capability. Given the field GF(q) and n/(q-1), LCD MDS codes of length n and dimension r are explicitly constructed over GF(q) for all r<n when n is odd and for all odd r<n when n is even. Series of asymptotically good LCD MDS codes are explicitly constructed. Efficient encoding and decoding algorithms exist for all the constructed codes. Linear complementary dual codes have importance in data storage, communications' systems and security.