I am interested in the following quantity. Suppose we are given a matrix $M\in \mathbb{F}_2^{m\times n}$ and a string $z\in \{0,1\}^n$. I am interested in finding the largest subset $S$ of rows in M such that the following holds: for every $i\in [n]$, there is $at$ $most$ one row in $v\in S$ such that $v_i\neq z_i$.I was wondering if this combinatorial notion has been used to characterize some complexity in literature? Any reference/ pointer is welcome. I am not interested in an algorithm to find the largest subset, but rather if such a combinatorial notion has been used to character some other complexity measure
reference request- property of subset of rows in a matrix
reference request;co.combinatorics;matrices;extremal combinatorics;boolean matrix