In this note we show that there exist exactly 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 implied by B_n such that A is non-full rank and the cardinality of R(A) equals 2~(n-2)+2~(n-3)+2~s.
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