Theoretical Foundations of Applied Discrete Mathematics

New series of $5$-configurations

M. M. Komiagin


Abstract: We consider $5$-configurations defined by their incident matrices over the field $\text{GF}(2)$, which must be nonsingular and contain exactly $5$ units in each row and each column, and the inverse matrix must also have this property. The relation between $5$-configurations of the $\mathcal{B}$ series and the $5$-configurations obtained by Abelian groups is indicated. A new series of $5$-configurations is presented. It is proved that this serie is not combinatorially equivalent to the previously known series of $5$-configurations. The diffusion characteristics of the incident matrix of $5$-configurations from the considered series are calculated.

Keywords: $k$-configurations, $k$-matrices, digraphs, Abelian groups, matrix diffusion characteristics.

UDC: 519.14

DOI: 10.17223/2226308X/18/6