ON THE MINIMAL COSET COVERINGS OF THE SET OF SINGULAR AND OF THE SET OF NONSINGULAR MATRICES

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Submitted: 2025-02-04; Published: 2025-02-04

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Abstract

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).