Quasi-Cyclic Codes

TL;DR

This paper surveys the algebraic structure and properties of quasi-cyclic codes, highlighting their significance in coding theory, including bounds, trace representations, and subfamily characterizations.

Contribution

It provides a comprehensive overview of the structural properties and applications of quasi-cyclic codes, including new asymptotic results and bounds.

Findings

Structural properties of quasi-cyclic codes elucidated

Asymptotic bounds derived for code parameters

Applications in trace representation and subfamily characterization

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.