29 citations · 139 across the 27 of their papers we have counts for
30 papers
Combinatorial designs, difference sets and bent functions as perfect colorings of graphs and multigraphs
V. N. Potapov, S. V. Avgustinovich
It is proved that 1) the indicator function of some onefold or multifold independent set in a regular graph is a perfect coloring if and only if the set attain the Delsarte--Hoffma…
Upper bounds on the numbers of binary plateaued and bent functions
Vladimir N. Potapov
The logarithm of the number of binary n-variable bent functions is asymptotically less than as n tends to infinity. Keywords: boolean function, Walsh--Hadamard transfo…
An upper bound on the number of frequency hypercubes
Denis S. Krotov, Vladimir N. Potapov
A frequency -cube is an -dimensional -by-...-by- array, where , filled by numbers with the property that each…
On extremal properties of perfect 2-colorings
Vladimir N. Potapov
A coloring of vertices of a graph is called perfect if, for every vertex, the collection of colors of its neighbors depends only on its own color. The correspondent color partition…
Embedding in MDS codes and Latin cubes
Vladimir N. Potapov
An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance and length can be embedded into an MDS code with t…
An asymptotic lower bound on the number of bent functions
V. N. Potapov, A. A. Taranenko, Yu. V. Tarannikov
A Boolean function on variables is said to be a bent function if the absolute value of all its Walsh coefficients is . Our main result is a new asymptotic lower bo…