Abstract
In this paper, we investigate the LCD repeated-root cyclic codes of length \(n=n'p^r\) over the finite field \(\mathbb {F}_q\), where gcd\((n',p)=1\). We give a necessary and sufficient condition for a repeated-root cyclic code to be LCD over \(\mathbb {F}_q\). We also determine the minimum distance of LCD repeated-root cyclic codes over \(\mathbb {F}_q\). Finally, we give the enumeration of LCD repeated-root cyclic codes of length n over \(\mathbb {F}_q\).
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This research is supported by the National Natural Science Foundation of China (Nos. 61370089, 61572168, 11501156) and the Anhui Provincial Natural Science Foundation (No. 1508085SQA198).
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Pang, B., Zhu, S. & Li, J. On LCD repeated-root cyclic codes over finite fields. J. Appl. Math. Comput. 56, 625–635 (2018). https://doi.org/10.1007/s12190-017-1118-z
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DOI: https://doi.org/10.1007/s12190-017-1118-z