29 citations · 53 across the 27 of their papers we have counts for
4 papers · 1 filter
On existence of perfect bitrades in Hamming graphs
I. Yu. Mogilnykh, F. I. Solov'eva
A pair of disjoint sets of vertices of a graph is called a perfect bitrade in if any ball of radius 1 in contains exactly one vertex in and or n…
A concatenation construction for propelinear perfect codes from regular subgroups of GA(r,2)
I. Yu. Mogilnykh, F. I. Solov'eva
A code is called propelinear if there is a subgroup of of order acting transitively on the codewords of . In the paper new propelinear perfect binary codes of…
Equitable 2-partitions of the Hamming graphs with the second eigenvalue
Ivan Mogilnykh, Alexandr Valyuzhenich
The eigenvalues of the Hamming graph are known to be , . The characterization of equitable 2-partitions of the Hamming graphs …
Perfect codes from PGL(2,5) in Star graphs
Ivan Mogilnykh
The Star graph is the Cayley graph of the symmetric group with the generating set $\{(1\mbox{ }i): 2\leq i\leq n \}$. Arumugam and Kala proved that $\{π\in Sym_n: π(1…