Abstract
In this paper, we obtain several new classes of \(p\)-ary bent functions, where \(p\) is a prime. The bentness of all these functions is characterized by some exponential sums, which have close relations with Kloosterman sums. Moreover, we obtain some concise criterions on the bentness of \(p\)-ary functions in some special cases. In addition, our work generalizes some main results obtained by Li et al. (IEEE Trans Inf Theory 59(3):1818–1831, 2013).
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Acknowledgments
We sincerely thank the anonymous reviewers for their helpful comments and suggestions. The work of H. Liu 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). The work of D. Zheng was supported by NSFC (Grant No. 11101131) and the Natural Science Foundation of Hubei Province under Grant 2014CFB537.
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Yu, L., Liu, H. & Zheng, D. On more bent functions from Dillon exponents. AAECC 26, 389–408 (2015). https://doi.org/10.1007/s00200-015-0258-3
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DOI: https://doi.org/10.1007/s00200-015-0258-3