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- W4287710742 abstract "We give an explicit construction of length-$n$ binary codes capable of correcting the deletion of two bits that have size $2^n/n^{4+o(1)}$. This matches up to lower order terms the existential result, based on an inefficient greedy choice of codewords, that guarantees such codes of size $Omega(2^n/n^4)$. Our construction is based on augmenting the classic Varshamov-Tenengolts construction of single deletion codes with additional check equations. We also give an explicit construction of binary codes of size $Omega(2^n/n^{3+o(1)})$ that can be list decoded from two deletions using lists of size two. Previously, even the existence of such codes was not clear." @default.
- W4287710742 created "2022-07-26" @default.
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- W4287710742 date "2020-07-21" @default.
- W4287710742 modified "2023-10-16" @default.
- W4287710742 title "Explicit two-deletion codes with redundancy matching the existential bound" @default.
- W4287710742 doi "https://doi.org/10.48550/arxiv.2007.10592" @default.
- W4287710742 hasPublicationYear "2020" @default.
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