On complementary dual quasi-twisted codes

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.