Quasi-Cyclic Codes (2007.16029v2)

Abstract: Quasi-cyclic codes form an important class of algebraic codes that includes cyclic codes as a special subclass. This chapter focuses on the algebraic structure of quasi-cyclic codes, first. Based on these structural properties, some asymptotic results, a few minimum distance bounds and further applications such as the trace representation and characterization of certain subfamilies of quasi-cyclic codes are elaborated. This survey will appear as a chapter in "A Concise Encyclopedia of Coding Theory" to be published by CRC Press.