In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic codes. We show a one-to-one correspondence between ℓ-quasi-cyclic codes of length mℓ and left ideals of M ℓ (Fq)[X]/(X m − 1). Then, we generalize BCH codes and evaluation codes in this context. We study their parameters and establish a key equation. Finally, we present a new [189,11, 125] F 4 code beating the known minimum distance for fixed length and dimension. Many codes with good parameters beating best known ones have been found from this latter.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.