The graph of minimal distances of bent functions and its properties

Результат исследования: Научные публикации в периодических изданияхстатья

6 Цитирования (Scopus)

Аннотация

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) ∈ E if the Hamming distance between f and g is equal to 2 k. It is shown that the maximum degree of the graph is equal to 2 k(2 1+ 1) (2 2+ 1) ⋯ (2 k+ 1) and all its vertices of maximum degree are quadratic bent functions. It is obtained that the degree of a vertex from Maiorana—McFarland class is not less than 2 2 k + 1- 2 k. It is proven that the graph is connected for 2 k= 2 , 4 , 6 , disconnected for 2 k≥ 10 and its subgraph induced by all functions EA-equivalent to Maiorana—McFarland bent functions is connected.

Язык оригиналаанглийский
Страницы (с-по)395-410
Число страниц16
ЖурналDesigns, Codes, and Cryptography
Том85
Номер выпуска3
DOI
СостояниеОпубликовано - 1 дек 2017

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