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September 10, 2025Open Access

On generator polynomial matrices of quasi-cyclic codes with linear complementary duals

Key Points

Necessary and sufficient conditions for linear complementary duals in quasi-cyclic codes are identified.
This research extends previous findings on cyclic codes to quasi-cyclic codes, enhancing the mathematical framework.
Various examples of optimal binary LCD quasi-cyclic codes are presented, illustrating practical applications.
Implications for future studies in coding theory are discussed, highlighting potential advancements in code design.

Abstract

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. (Mon,) studied this question.

synapsesocial.com/papers/68c182609b7b07f3a060f4bf https://doi.org/https://doi.org/10.13069/jacodesmath.v12i3.324