On inequalities for the parameters of combinatorial matrices of a special form (Q1878738)

The paper considers the class of \(2^k\times p\) matrices \(B\) whose entries assume the values in the set \(\{1,2, *\}\) of symbols such that the following conditions hold: (a) for any two rows with numbers \(i_1\) and \(i_2\), there exists a column with number \(j\) such that \(b_{i_1,j}=1\), \(b_{i_2,j}=2\) or \(b_{i_1,j}= 2\), \(b_{i_2,j}=1\); (b) for any row with number \(i\), the inequality \(\sum_{j=1}^p b_{ij}\leq t\) holds for a certain natural number \(t\) given in advance; (c) in each row, the number of units does not exceed \(k_0\), a given natural number. The author obtains lower estimates for the ratio \(k/(t+k)\),