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arXiv · 1910.12247

Optimal $k$-Deletion Correcting Codes

Jin Sima·Jehoshua Bruck
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Abstract

Levenshtein introduced the problem of constructing $k$-deletion correcting codes in 1966, proved that the optimal redundancy of those codes is $O(k\log N)$, 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 $8k\log n +o(\log n)$ and encoding/decoding algorithms of complexity $O(n^{2k+1})$ for constant $k$.

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Jin Sima, Jehoshua Bruck. 2019-10-27. Optimal $k$-Deletion Correcting Codes. https://arxiv.org/abs/1910.12247

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