Abstract
We obtain two kinds of new results on nonexistence of generalized bent functions (GBFs). Based on the results of Feng, Liu and Ma, we use Schmidt’s field descent method to get the first kind. For the second kind, we use both decomposition law in cyclotomic fields and bent requirements to prove that no GBFs with type \([3,\,2\cdot 23^{e}]\) exist.
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Acknowledgments
The work of this paper was supported by the NNSF of China (Grants Nos. 11071285, 61121062), 973 Project (2011CB302401) and the National Center for Mathematics and Interdisciplinary Sciences, CAS.
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Communicated by A. Pott.
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Jiang, Y., Deng, Y. New results on nonexistence of generalized bent functions. Des. Codes Cryptogr. 75, 375–385 (2015). https://doi.org/10.1007/s10623-014-9923-y
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DOI: https://doi.org/10.1007/s10623-014-9923-y
Keywords
- Field descent method
- Generalized bent functions
- Cyclotomic fields
- Prime ideal factorization
- Principal ideal
- Ideal norm