Paper 2015/1203
The graph of minimal distances of bent functions and its properties
Nikolay Kolomeec
Abstract
A notion of the graph of minimal distances of bent functions is introduced. It is an undirected graph ($V$, $E$) where $V$ is the set of all bent functions in $2k$ variables and $(f, g) \in E$ if the Hamming distance between $f$ and $g$ is equal to $2^k$ (it is the minimal possible distance between two different bent functions). The maximum degree of the graph is obtained and it is shown that all its vertices of maximum degree are quadratic. It is proven that a subgraph of the graph induced by all functions affinely equivalent to Maiorana---McFarland bent functions is connected.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- Boolean functionsbent functionsthe minimal distanceaffinity
- Contact author(s)
- nkolomeec @ gmail com
- History
- 2015-12-18: received
- Short URL
- https://ia.cr/2015/1203
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2015/1203,
author = {Nikolay Kolomeec},
title = {The graph of minimal distances of bent functions and its properties},
howpublished = {Cryptology ePrint Archive, Paper 2015/1203},
year = {2015},
note = {\url{https://eprint.iacr.org/2015/1203}},
url = {https://eprint.iacr.org/2015/1203}
}
