Reed-Solomon codes have gained a lot of interest due to its encoding simplicity, well structuredness and list-decoding capability [6] in the classical setting. This interest also translates to other metric setting, including the insertion and deletion (insdel for short) setting which is used to model synchronization errors caused by positional information loss in communication systems. Such interest is supported by the construction of a deletion correcting algorithm of insdel Reed-Solomon code in [22] which is based on the Guruswami-Sudan decoding algorithm [6]. Nevertheless, there have been few studies [3] on the insdel error-correcting capability of Reed-Solomon codes.

In this paper, we discuss a criterion for a 2-dimensional insdel Reed-Solomon codes to have optimal asymptotic error-correcting capabilities, which are up to their respective lengths. Then we provide explicit constructions of 2-dimensional insdel Reed-Solomon codes that satisfy the established criteria. The family of such constructed codes can then be shown to extend the family of codes with asymptotic error-correcting capability reaching their respective lengths provided in [3, Theorem 2] which provide larger error-correcting capability compared to those defined in [25].

里德-所罗门码由于其在经典环境中的编码简单，结构良好和列表解码能力[6]而引起了人们的极大兴趣。这种兴趣还转换为其他度量标准设置，包括用于模拟由通信系统中的位置信息丢失引起的同步错误的插入和删除（简称insdel）设置。在[22]中基于Guruswami-Sudan解码算法[6]的insdel Reed-Solomon码删除校正算法的构建，支持了这种兴趣。尽管如此，关于里德-所罗门码的insdel纠错能力的研究很少[3]。

在本文中，我们讨论了二维insdel Reed-Solomon码的准则，该准则具有最佳的渐近纠错能力，并能达到各自的长度。然后，我们提供满足既定标准的二维insdel Reed-Solomon码的显式构造。然后，可以显示出这种构造的代码系列可以扩展具有渐近纠错能力的代码系列，使其达到[3，定理2]中提供的相应长度，与[25]中定义的纠错能力相比，它们可以提供更大的纠错能力。