Quasi-cyclic Codes: An overview

Quasi-cyclic (QC) linear codes over finite fields constitute an important class of linear block codes. They are a remarkable generalization of cyclic codes and, in contrast to them, several QC codes attain the highest minimum Hamming distance possible for a given length and dimension. In this talk we review basic aspects of QC codes and three perspectives of their algebraic structure. Some preliminary results on generator and parity check matrices for these codes over extension fields will be also presented.