Existence of perfect 4-deletion-correcting codes with length six (Q697639)

Let \(Q\) be an alphabet of size \(v\) and \(Q^k\) the set of all vectors (or words) of length \(k\) over \(Q\). A subset \(C\subseteq Q^k\) is said to be a perfect \((k-2)\)-deletion-correcting code over \(Q\), or a \(T^*(2,k,v)\)-code, if every word of \(Q^2\) can be obtained by deleting \(k-2\) letters from exactly one word of \(C\). The authors introduce in this paper the notion of a directed group divisible quasidesign, and they use this to show that a \(T^*(2,6,v)\)-code exists for all positive integers \(v\), except possibly when \(v\in \{173,178,203,208\}\).