Abstract
Cyclic codes over an infinite family of rings are defined. The general properties of cyclic codes over these rings are studied, in particular nontrivial one-generator cyclic codes are characterized. It is also proved that the binary images of cyclic codes over these rings under the natural Gray map are binary quasi-cyclic codes of index 2k. Further, several optimal or near optimal binary codes are obtained from cyclic codes over R k via this map.
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Communicated by W. H. Haemers.
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Dougherty, S.T., Karadeniz, S. & Yildiz, B. Cyclic codes over R k . Des. Codes Cryptogr. 63, 113–126 (2012). https://doi.org/10.1007/s10623-011-9539-4
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DOI: https://doi.org/10.1007/s10623-011-9539-4