Optimal Two-Dimensional Reed–Solomon Codes Correcting Insertions and Deletions
IEEE Transactions on Information Theory(2023)
摘要
Constructing Reed–Solomon (RS) codes that can correct insertions and
deletions (insdel errors) has been considered in numerous recent works. For the
special case of two-dimensional RS-codes, it is known [CST23] that an [n,2]_q
RS-code that can correct from n-3 insdel errors satisfies that
q=Ω(n^3). On the other hand, there are several known constructions of
[n,2]_q RS-codes that can correct from n-3 insdel errors, where the
smallest field size is q=O(n^4). In this short paper, we construct [n,2]_q
Reed–Solomon codes that can correct n-3 insdel errors with q=O(n^3),
thereby resolving the minimum field size needed for such codes.
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