Construction of Quasi-Cyclic Product Codes

Abstract

Linear quasi-cyclic product codes over finite fields are investigated. Given the generating set in the form of a reduced Gröbner basis of a quasi-cyclic component code and the generator polynomial of a second cyclic component code, an explicit expression of the basis of the generating set of the quasicyclic product code is given. Furthermore, the reduced Gröbner basis of a one-level quasi-cyclic product code is derived.