The graph of minimal distances of bent functions and its properties

Nikolay Kolomeec

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 $2 k$ 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 functions bent functions the minimal distance affinity
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},
      url = {https://eprint.iacr.org/2015/1203}
}