Abstract
Let \(m\), \(k\) be positive integers, \(p\) be an odd prime and \(\pi \) be a primitive element of \({\mathbb {F}}_{p^m}\). In this paper, we determine the weight distribution of a family of cyclic codes \({\mathcal {C}}_t\) over \({\mathbb {F}}_p\), whose duals have two zeros \(\pi ^{-t}\) and \(-\pi ^{-t}\), where \(t\) satisfies \(t\equiv \frac{p^k+1}{2}p^\tau \ (\mathrm{mod}\ \frac{p^m-1}{2}) \) for some \(\tau \in \{0,1,\ldots , m-1\}\).
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Acknowledgments
This work was supported by NSFC (Grant No. 11171370) and self-determined research funds of CCNU from the colleges’ basic research and operation of MOE (Grant No. CCNU14F01004). We sincerely thank the anonymous reviewers for their helpful comments and suggestions.
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Communicated by J. D. Key.
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Yu, L., Liu, H. The weight distribution of a family of \(p\)-ary cyclic codes. Des. Codes Cryptogr. 78, 731–745 (2016). https://doi.org/10.1007/s10623-014-0029-3
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DOI: https://doi.org/10.1007/s10623-014-0029-3