Nonexistence of generalized bent functions and the quadratic norm form equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
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2018
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| _version_ | 1866917360159424512 |
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| author | Lv, Chang Zhu, Yuqing |
| author_facet | Lv, Chang Zhu, Yuqing |
| contents | We present a new result on the nonexistence of generalized bent functions (GBFs)from (Z/tZ)^n to Z/tZ (called type [n, t]) for a large class. Assume p is an odd prime number. By showing certain quadratic norm form equations having no integral points, we obtain a universalresult on the nonexistence of GBFs with type [n,2p^e] when p and n satisfy a certain inequality, and by computational methods with a widely accepted hypothesis, Generalized Riemann Hypothesis, we also achieve some results on the nonexistence of GBFs for relatively small p. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1804_01292 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Nonexistence of generalized bent functions and the quadratic norm form equations Lv, Chang Zhu, Yuqing Information Theory Number Theory 11D57, 11D09, 11R29, 94A15 We present a new result on the nonexistence of generalized bent functions (GBFs)from (Z/tZ)^n to Z/tZ (called type [n, t]) for a large class. Assume p is an odd prime number. By showing certain quadratic norm form equations having no integral points, we obtain a universalresult on the nonexistence of GBFs with type [n,2p^e] when p and n satisfy a certain inequality, and by computational methods with a widely accepted hypothesis, Generalized Riemann Hypothesis, we also achieve some results on the nonexistence of GBFs for relatively small p. |
| title | Nonexistence of generalized bent functions and the quadratic norm form equations |
| topic | Information Theory Number Theory 11D57, 11D09, 11R29, 94A15 |
| url | https://arxiv.org/abs/1804.01292 |