On the minimal distance graph connectivity for bent functions
For the set B 2k of all bent functions in 2k variables, the graph GB 2k is defined. The vertices in GB 2k are all functions in B 2k and two of them are adjacent if and only if the Hamming distance between them is equal to 2 . It is proved that, for k = 1, 2, 3, the graph GB2k is connected and, for any k, the subgraph of GB2k induced by the subset of all vertices being affine equivalent to Maiorana - McFarland bent functions is also connected.
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Keywords
the minimal distance, bent functions, Boolean functions, бент-функции, минимальное расстояние, булевы функцииAuthors
| Name | Organization | |
| Kolomeec N. A. | Institute of Mathematics. Sobolev SB RAS (Novosibirsk) | nkolomeec@gmail.com |
References
Коломеец Н.А. Верхняя оценка числа бент-функций на расстоянии 2k от произвольной бент-функции от 2k переменных // Прикладная дискретная математика. 2014. №3. С.28-39.
Tokareva N. N. Bent Functions: Results and Applications to Cryptography. Acad. Press. Elsevier, 2015.
McFarland R. L. A family of difference sets in non-cyclic groups // J. Combin. Theory. Ser. A. 1973. V. 15. P. 1-10.
Rothaus O. On bent functions // J. Combin. Theory. Ser.A. 1976. V.20. No.3. P. 300-305.
On the minimal distance graph connectivity for bent functions | Applied Discrete Mathematics. Supplement. 2015. № 8.
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