On complementary dual quasi-twisted codes

Abstract

A linear complementary-dual (LCD) code C is a linear code whose dual code $$C^{\perp }$$ satisfies $$C \cap C^{\perp }=\{0\}$$ . In this work we characterize some classes of LCD q-ary $$(\lambda , l)$$ -quasi-twisted (QT) codes of length $$n=ml$$ with $$(m,q)=1$$ , $$\lambda \in F_{q} \setminus \{0\}$$ and $$\lambda \ne \lambda ^{-1}$$ . We show that every $$(\lambda ,l)$$ -QT code C of length $$n=ml$$ with $$dim(C)<m$$ or $$dim(C^{\perp })<m$$ is an LCD code. A sufficient condition for r-generator QT codes is provided under which they are LCD. We show that every maximal 1-generator $$(\lambda ,l)$$ -QT code of length $$n=ml$$ with $$l>2$$ is either an LCD code or a self-orthogonal code and a sufficient condition for this family of codes is given under which such a code C is LCD. Also it is shown that every maximal 1-generator $$(\lambda ,2)$$ -QT code is LCD. Several good and optimal LCD QT codes are presented.