Constructions for Perfect 5-Deletion-Correcting Codes of Length$7$

There are two kinds of perfect (k-t)-deletion-correcting codes with words of length k over an alphabet of size v, those where the coordinates may be equal and those where all coordinates must be different. We call these two kinds of codes T*(t,k,v)-codes and T(t,k,v)-codes respectively. Both a T*(t,k,v)-code and a T(t,k,v)-code are capable of correcting any combination of up to (k-t) deletions and insertions of letters occurred in transmission of codewords. In this correspondence, we consider constructions for the codes from directed designs. By means of these constructions, the existence of a T(2,7,v)-code is settled for all positive integers v with the exception of 68 values of v; T^*(2,7,v)-codes are constructed for all integers vges2350. A large number of explicit constructions for T^*(2,7,v)-codes with v<2350 are also presented