Geodesic
On Multiple Deletion Codes
Serdica Journal of Computing, Tome 1 (2007) no. 1, pp. 13-26

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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.
Keywords: Insertion/Deletion Codes, Varshamov-Tennengolts Codes, Multiple Insertion/Deletion Codes 
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Landjev, Ivan; Haralambiev, Kristiyan. On Multiple Deletion Codes. Serdica Journal of Computing, Tome 1 (2007) no. 1, pp. 13-26. http://geodesic.mathdoc.fr/item/SJC_2007_1_1_a2/