Binary linear complementary dual codes

02/20/2018

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by   Masaaki Harada, et al.

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Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual [n,k] codes with the largest minimum weight among all binary linear complementary dual [n,k] codes. We characterize binary linear complementary dual codes with the largest minimum weight for small dimensions. A complete classification of binary linear complementary dual [n,k] codes with the largest minimum weight is also given for 1 < k < n < 16.