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 v >= 2350. A large number of explicit constructions for T * (2, 7, v) -codes with v < 2350 are also presented.
directed design directed balanced incomplete block design (dbibd) deletion/insertion-correcting code perfect deletion-correcting code