On the Cardinalities of the Row spaces of Non-full Rank Boolean Matrices

n

-2 integers 2^{n -2}+2^{n -3}+2^s, where s=0,1,2,...,n-3, in the interval (2^{n -2}+2^{n -3},2^{n -1}] such that these integers are the cardinalities of row spaces R(A) of non-full rank Boolean matrices A of order n. We also show that for each s, where s=0,1,2,...,n-3, there exists A epsilon B _n such that A is non-full rank and the cardinality of R(A) equals 2^{n -2}+2^{n -3}+2^s.