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Constructing Reed--Solomon (RS) codes that can correct insertions anddeletions (insdel errors) has been considered in numerous recent works. For thespecial 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$q=\Omega(n^3)$. On the other hand, there are several known constructions of$[n,2]_q$ RS-codes that can correct from $n-3$ insdel errors, where thesmallest 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.

Optimal Two-Dimensional Reed--Solomon Codes Correcting Insertions and Deletions