Design theory
On the construction of perfect deletion-correcting codes using design theory
Designs, Codes and Cryptography
Existence of Perfect 3-Deletion-CorrectingCodes
Designs, Codes and Cryptography
A Combinatorial Construction for PerfectDeletion-Correcting Codes
Designs, Codes and Cryptography
Construction of deletion correcting codes using generalized Reed---Solomon codes and their subcodes
Designs, Codes and Cryptography
Some combinatorial constructions for optimal perfect deletion-correcting codes
Designs, Codes and Cryptography
Spectrum of Sizes for Perfect Deletion-Correcting Codes
SIAM Journal on Discrete Mathematics
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By a T*(2, k, v)-code we mean a perfect4-deletion-correcting code of length 6 over an alphabet of size v, which is capable of correcting anycombination of up to 4 deletions and/or insertions of letters that occur in transmission of codewords. Thethird author (DCC Vol. 23, No. 1) presented a combinatorial construction for such codes and prove thata T*(2, 6, v)-code exists for all positive integers v≢ 3 (mod 5), with 12 possible exceptions of v. In this paper, the notion of a directedgroup divisible quasidesign is introduced and used to show that a T*(2, 6,v)-code exists for all positive integers v ≡ 3 (mod 5), except possiblyfor v ∈ {173, 178, 203, 208}. The 12 missing cases for T*(2,6, v)-codes with v ≢ 3 (mod 5) are also provided, thereby the existenceproblem for T*(2, 6, v)-codes is almost complete.