Gaps in the Cardinalities of Row Spaces of Boolean Matrices

摘要

In this paper we study the cardinalities of row spaces of Boolean matrices. We obtain the following main results: For the cardinalities of row spaces of Boolean matrices of order n, if n ≥ 8, then 2~(n-1) - k, where k = 1, 2, 3, are gaps; if n = 7, then 2~(n-1) -k, where k = 1, 3, are gaps. This also implies that Konieczny's conjecture [2] is not true.