On Optimal k-Deletion Correcting Codes

Abstract

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

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