Construction of Quasi-Cyclic Product Codes
This work addresses a theoretical problem in coding theory for researchers, but it appears incremental as it builds on existing quasi-cyclic and cyclic component codes.
The paper tackled constructing linear quasi-cyclic product codes over finite fields by providing explicit expressions for the basis of their generating set and deriving the reduced Gröbner basis for one-level quasi-cyclic product codes, based on given generating sets and generator polynomials of component codes.
Linear quasi-cyclic product codes over finite fields are investigated. Given the generating set in the form of a reduced Gr{ö}bner 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 quasi-cyclic product code is given. Furthermore, the reduced Gr{ö}bner basis of a one-level quasi-cyclic product code is derived.