PERFECT ERROR-CORRECTING DATABASES

An n×m matrix is called a t-error-correcting database if after deleting any t columns one can still distinguish the rows. It is perfect if after omitting any t+1 columns two identical rows are obtained. (Stating with another terminology, the system of minimal keys induced by A is the system of all (n-t)-element subsets of an n-element set.). Let ft(n) denote the minimum number of rows in a perfect t-error-correcting database of length n. We show that f2(n)=Θ(n2), and in general Ω(n(2t+1){plus 45 degree rule}3)≤ft(n)≤O(nt) for t≥3, whenever n→∞. © 1990.