Abstract
By constructing a Gray map, a class of constacyclic codes over ring R = R+vR is studied. Using cyclic codes and negacyclic codes of length p s over ring R, the structure of (1−2v)-constacyclic codes and dual codes of length p s over ring R are given, the Gray images of (1 − 2v)-constacyclic codes in a particular case are also studied. It is shown that linear codes of length p s over ring R are (1−2v)-constacyclic codes if and only if their Gray images are distance-invariant cyclic codes of length 2p s over ring R.
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This research was supported by the National Natural Science Foundation of China under Grant No. 61370089.
This paper was recommended for publication by Editor LI Ziming.
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Huang, L., Zhu, S. A class of constacyclic codes over ring R + vR . J Syst Sci Complex 29, 805–813 (2016). https://doi.org/10.1007/s11424-015-4108-y
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DOI: https://doi.org/10.1007/s11424-015-4108-y