Properties of a bent function construction by a subspace of an arbitrary dimension
Let f be a bent function in 2k variables, L be an affine subspace of F2k, and IndL be a Boolean function with values 1 on L. Here, we study the properties of the function f ф IndL. Particularly, we give some necessary and sufficient conditions under which the increase or decrease of the dimension of L by 1 doesn't change the property bent of f ф IndL. We prove that if the function f (x1,..., x2k) ф x2k+1x2k+2 ф Ind^ is a bent function and U is an affine subspace, then the function f ф IndL is a bent function for some affine subspace L of dimension dim U - 1 or dim U - 2. An example of bent function f in 10 variables for which f ф IndL is a bent function for only dim L ( {9,10} is provided.
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Keywords
affinity, subspaces, bent functions, Boolean functions, аффинность, бент-функции, подпространства, булевы функцииAuthors
| Name | Organization | |
| Kolomeec N. A. | Sobolev Institute of Mathematics | kolomeec@math.nsc.ru |
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