Abstract
In this paper, we study minimal cyclic codes of length \(\ell ^{m}\) over a finite field \(\mathbb{F }_q\), where \(\ell \) is a prime divisor of \(q-1\) and \(m\) is a positive integer. Explicit expressions for the primitive idempotents, check polynomials, minimum Hamming distances and the dimensions of these codes are obtained.
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Acknowledgments
The authors would like to deeply thank the referees for their very careful reading and many valuable comments that helped us improve this paper. The authors also thank NSFC for the support through Grant No. 11171370, and Research Funds of CCNU, Grant No. 11A02014.
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Communicated by C. Mitchell.
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Chen, B., Liu, H. & Zhang, G. A class of minimal cyclic codes over finite fields. Des. Codes Cryptogr. 74, 285–300 (2015). https://doi.org/10.1007/s10623-013-9857-9
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DOI: https://doi.org/10.1007/s10623-013-9857-9