This work demonstrates conditions for linear complementary duals in quasi-cyclic codes, suggesting broader applications.
Using notion of generator polynomial matrices of quasi-cyclic codes, we show a necessary and sufficient condition for which these codes are to be linear complementary dual. This extends the well-known result by Yang and Massey on cyclic codes to quasi-cyclic codes. As an application we present various examples of optimal binary LCD quasi-cyclic codes.
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Ojiro et al. (2025) studied this question.
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