Abstract
By constructing a Gray map, constacyclic codes of arbitrary lengths over ring \(R = Z_{p^m } + vZ_{p^m }\) are studied, where v 2 = v The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular, (1+(v+1)αp)-constacyclic codes over R are classified in terms of generator polynomial, where α is a unit of \(Z_{p^m }\).
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Supported by the National Natural Science Foundation of China (No. 61370089).
Huang Lei, born in 1989, male, Master Degree.
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Huang, L., Zhu, S. Constacyclic codes of arbitrary lengths over ring \(Z_{p^m } + vZ_{p^m }\) . J. Electron.(China) 31, 222–226 (2014). https://doi.org/10.1007/s11767-014-3167-x
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DOI: https://doi.org/10.1007/s11767-014-3167-x