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 $q=\Omega(n^3)$. On the other hand, there are several known constructions of $[n,2]_q$ RS-codes that can correct from $n-3$ insdel errors, where 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.

翻译：构造能够纠正插入与删除错误（简称insdel错误）的里德-所罗门（RS）码是近年多项研究的课题。针对二维RS码的特例，文献[CST23]已证明：一个能纠正$n-3$个insdel错误的$[n,2]_q$ RS码需满足$q=\Omega(n^3)$。另一方面，现有若干$[n,2]_q$ RS码的构造可纠正$n-3$个insdel错误，其最小域大小为$q=O(n^4)$。本文通过构造域大小为$q=O(n^3)$的$[n,2]_q$里德-所罗门码，实现了对$n-3$个insdel错误的纠正，从而确定了此类码所需的最小域大小。