Abstract
In this paper, the period distribution of cyclic codes over R = F q + uF q + ⋯ + u m−1 F q is studied, where u m = 0 and q is a prime power. A necessary and sufficient condition for the existence of period of cyclic codes over R is given. The period distributions of cyclic codes over R and their dual codes are determined by employing generator polynomial. The counting formulas of the period distributions of cyclic codes over R and their dual codes are obtained.
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Supported by the National Natural Science Foundation of China (No. 61370089), Fundamental Research Funds for the Central Universities (Nos. 2013HGCH0024, J2014HG-XJ0073), and Specialized Research Fund for the Doctoral Program of Hefei University of Technology (No. JZ2014-HGBZ0029).
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Li, P., Zhong, J. & Zhu, S. Period distribution of cyclic codes over F q + uF q + ⋯ + u m−1 F q . J. Electron.(China) 31, 547–551 (2014). https://doi.org/10.1007/s11767-014-4017-6
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DOI: https://doi.org/10.1007/s11767-014-4017-6