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Construction of Quasi-Cyclic Product Codes (1501.06543v1)
Published 26 Jan 2015 in cs.IT, cs.CR, cs.DM, math.CO, math.IT, and math.NT
Abstract: Linear quasi-cyclic product codes over finite fields are investigated. Given the generating set in the form of a reduced Gr{\"o}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{\"o}bner basis of a one-level quasi-cyclic product code is derived.