Quasi-twisted codes as invariant subspaces

Quasi-twisted codes extend the concept of quasi-cyclic codes, offering a rich algebraic structure relative to general linear codes and demonstrating strong asymptotic properties. This paper investigates the algebra properties of quasi-twisted codes over the finite field $ \mathbb{F}_q, $ treating them as invariant subspaces under a specific linear transformation. We also establish a lower bound for the minimum distance of $ 1 $-generator quasi-twisted codes, which in some cases exceeds the known BCH-type bound.