On Optimal <i>k</i>-Deletion Correcting Codes

Levenshtein introduced the problem of constructing k-deletion correcting codes in 1966, proved that optimal redundancy those is O(k log N) for constant k, and proposed an single-deletion code (using so-called VT construction). However, remained open. Our key contribution a major step towards complete solution to this longstanding open k. We present has 8 klog N + o(log when k = o(?{loglog N}) encoding/decoding algorithms complexity O(N 2 k+1 ).