In 1965 Levenshtein introduced the deletion correcting codes and found an asymptotically optimal family of 1-deletion correcting codes. During the years there has been a little or no research on t-deletion correcting codes for larger values of t. In this paper, we consider the problem of finding the maximal cardinality L2(n;t) of a binary t-deletion correcting code of length n. We construct an infinite family of binary t-deletion correcting codes. By computer search, we construct t-deletion codes for t = 2;3;4;5 with lengths n ≤ 30. Some of these codes improve on earlier results by Hirschberg-Fereira and Swart-Fereira. Finally, we prove a recursive upper bound on L2(n;t) which is asymptotically worse than the best known bounds, but gives better estimates for small values of n.
[1]
Vladimir I. Levenshtein,et al.
Binary codes capable of correcting deletions, insertions, and reversals
,
1965
.
[2]
Hendrik C. Ferreira,et al.
On multiple insertion/Deletion correcting codes
,
2002,
IEEE Trans. Inf. Theory.
[3]
Mireille Régnier,et al.
Tight Bounds on the Number of String Subsequences DANIEL S
,
2000
.
[4]
Hendrik C. Ferreira,et al.
A note on double insertion/deletion correcting codes
,
2003,
IEEE Trans. Inf. Theory.
[5]
Vladimir I. Levenshtein,et al.
Efficient Reconstruction of Sequences from Their Subsequences or Supersequences
,
2001,
J. Comb. Theory A.
[6]
N.J.A. Sloane,et al.
On Single-Deletion-Correcting Codes
,
2002,
math/0207197.