1. One generator quasi-cyclic codes over
- Author
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Siap, Irfan, Abualrub, Taher, and Yildiz, Bahattin
- Subjects
- *
MAPS , *LINEAR systems , *CODING theory , *SET theory , *RANKING , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we study quasi-cyclic codes over the ring where . By exploring their structure, we determine the type of one generator quasi-cyclic codes over R and the size by giving a minimal spanning set. We also determine the rank and introduce a lower bound for the minimum distance of free quasi-cyclic codes over . We include some examples of quasi-cyclic codes of various lengths over . In particular, we obtain a family of 2-quasi-cyclic codes from cyclic codes over the ring . Finally, using the Gray map we obtain a family of optimal binary linear codes as the images of quasi-cyclic codes over R. [Copyright &y& Elsevier]
- Published
- 2012
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