Quasi-cyclic codes as cyclic codes over a family of local rings |
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| Institution: | 1. Department of Mathematics, University of Scranton, Scranton, PA 18510, USA;2. Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Spain |
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| Abstract: | We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the Hamming space via the Gray map. We use the Gray map to produce optimal linear codes that are quasi-cyclic. |
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| Keywords: | Quasi-cyclic codes Codes over rings |
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