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- W2901206303 abstract "Let p be an odd prime, let a be a positive integer, let m be an odd positive integer, and suppose that a generalized bent function from Z 2 p a m to Z 2 p a exists. We show that this implies m ≠ 1 , p ≤ 2 2 m + 2 m + 1 , and ord p ( 2 ) ≤ 2 m − 1 . We obtain further necessary conditions and prove that p = 7 if m = 3 and p ∈ { 7 , 23 , 31 , 73 , 89 } if m = 5 . Our results are based on new tools for the investigation of cyclotomic integers of prescribed complex modulus, including “minimal aliases” invariant under automorphisms, and bounds on the ℓ 2 -norms of their coefficient vectors. These methods have further applications, for instance, to relative difference sets, circulant Butson matrices, and other kinds of bent functions." @default.
- W2901206303 created "2018-11-29" @default.
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- W2901206303 date "2019-04-01" @default.
- W2901206303 modified "2023-10-12" @default.
- W2901206303 title "Nonexistence results on generalized bent functions <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msubsup><mml:mrow><mml:mi mathvariant=double-struck>Z</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=false>→</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=double-struck>Z</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math> with odd m…" @default.
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- W2901206303 doi "https://doi.org/10.1016/j.jcta.2018.11.007" @default.
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