Abstract
We obtain some new nonexistence results of generalized bent functions from \({\mathbb {Z}}^n_q\) to \({\mathbb {Z}}_q\) (called type [n, q]) in the case that there exist cyclotomic integers in \( {\mathbb {Z}}[\zeta _{q}]\) with absolute value \(q^{\frac{n}{2}}\). This result generalizes two previous nonexistence results \([n,q]=[1,2\times 7]\) of Pei (Lect Notes Pure Appl Math 141:165–172, 1993) and \([3,2\times 23^e]\) of Jiang and Deng (Des Codes Cryptogr 75:375–385, 2015). We also remark that by using a same method one can get similar nonexistence results of GBFs from \({\mathbb {Z}}^n_2\) to \({\mathbb {Z}}_m\).
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Acknowledgements
The authors thank the anonymous referees for many helpful corrections and suggestions, many of which have been incorporated into this version of the paper. The authors are indebted to the editor Alexander Pott for his thorough careful reading and valuable suggestions. The authors also thank Yupeng Jiang, Chang Lv and Jiangshuai Yang for helpful discussions. The work of this paper was supported by the NNSF of China (Grant No. 11471314) and the National Center for Mathematics and Interdisciplinary Sciences, CAS.
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Li, J., Deng, Y. Nonexistence of two classes of generalized bent functions. Des. Codes Cryptogr. 85, 471–482 (2017). https://doi.org/10.1007/s10623-016-0319-z
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DOI: https://doi.org/10.1007/s10623-016-0319-z