ON THE MINIMAL COSET COVERINGS OF THE SET OF SINGULAR AND OF THE SET OF NONSINGULAR MATRICES
It is determined minimum number of cosets over linear subspaces in F_q necessary to cover following two sets of A (n × n) matrices. For one of the set of matrices A = 0 and for the other set A eq 0 . It is proved that for singular matrices this number is equal to 1 + q + q^2 + … + q^n-1 and for the nonsingular matrices it is equal to (q^n - 1)(q^n - q)(q^n - q^2) … (q^n - q^n-1) / q^n2 . , number=1 (245), journal=Proceedings of the YSU A: Physical and Mathematical Sciences, author=Minasyan, A.V., year=2018, month=Apr., pages=8–11