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2023-ary quasigroups and related topics
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Some results on matrices that are extremal for existence of polyplex A. A. Taranenko |
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Abstract: A polyplex of size A It is easy to prove that the maximum size of a polyplex in a matrix is equal to the minimal size of the covering of the matrix by hyperplanes. It is shown that any extremal matrix for can be encoded by an optimal covering by facets. Some necessary and sufficient conditions are obtained to cover with hyperplanes an extremal matrix. Also, several hypotheses have been put forward on the properties of extremal matrices. |