Optimal k-Deletion Correcting Codes

10/27/2019

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by   Jin Sima, et al.

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Levenshtein introduced the problem of constructing k-deletion correcting codes in 1966, proved that the optimal redundancy of those codes is O(klog N), 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 solution to this longstanding open problem. We present a k-deletion correcting code that has redundancy 8klog n +o(log n) and encoding/decoding algorithms of complexity O(n^2k+1) for constant k.