ON THE MINIMAL COSET COVERINGS OF THE SET OF SINGULAR AND OF THE SET OF NONSINGULAR MATRICES
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ON THE MINIMAL COSET COVERINGS OF THE SET OF SINGULAR AND OF THE SET OF NONSINGULAR MATRICES Ashot Minasya
It is determined minimum number of cosets over linear subspaces in Fq necessary to cover following two sets of A(n×n) matrices. For one of the set of matrices detA=0 and for the other set detA≠0. It is proved that for singular matrices this number is equal to 1+q+q2+…+qn−1 and for the nonsingular matrices it is equal to (qn−1)(qn−q)(qn−q2)⋯(qn−qn−1)/q(n2).
DOI: 10.46991/PYSU:A/2018.52.1.008 Physical and Mathematical Sciences, 52(1 (245) 8-11
