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Generalizations of Cole's Systems

Gizatullin, Marat (1996)

Serdica Mathematical Journal

There are four resolvable Steiner triple systems on fifteen elements. Some generalizations of these systems are presented here.

Generalized indices of Boolean matrices

Bo Zhou (2002)

Czechoslovak Mathematical Journal

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.

Generalized Whitney partitions

Michał Rams (2000)

Fundamenta Mathematicae

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.

Generating quasigroups for cryptographic applications

Czesław Kościelny (2002)

International Journal of Applied Mathematics and Computer Science

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...

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