GBRDs with block size three over 2-groups, semi-dihedral groups and nilpotent groups.
There are four resolvable Steiner triple systems on fifteen elements. Some generalizations of these systems are presented here.
We obtain upper bounds for generalized indices of matrices in the class of nearly reducible Boolean matrices and in the class of critically reducible Boolean matrices, and prove that these bounds are the best possible.
We prove that the upper Minkowski dimension of a compact set Λ is equal to the convergence exponent of any packing of the complement of Λ with polyhedra of size not smaller than a constant multiple of their distance from Λ.
A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both the plaintext and the ciphertext. From the practical viewpoint, the most important quasigroups are of...