A Combinatorial Construction for Perfect Deletion-Correcting Codes

By a T ^*(2, k, v)-code we mean a perfect(k-2)-deletion-correcting code of length k over an alphabet ofsize v, which is capable of correcting any combination of up to(k-2) deletions and insertions of letters occured in transmission ofcodewords. In this paper, we provide a combinatorial construction forT ^*(2, k, v-codes. As an application, we show that aT ^*(2, 6, v-code exists for all positive integersv 3 (mod 5), with at most 12 possible exceptions of v. In theprocedure, a result on incomplete directed BIBDs is also established which is ofinterest in its own right.