  Insertion and deletion (insdel for short) errors are synchronization errors
in communication systems caused by the loss of positional information in the
message. Reed-Solomon codes have gained a lot of interest due to its encoding
simplicity, well structuredness and list-decoding capability in the classical
setting. This interest also translates to the insdel metric setting, as the
Guruswami-Sudan decoding algorithm can be utilized to provide a deletion
correcting algorithm in the insdel metric. Nevertheless, there have been few
studies on the insdel error-correcting capability of Reed-Solomon codes. Our
main contributions in this paper are explicit constructions of two families of
2-dimensional Reed-Solomon codes with insdel error-correcting capabilities
asymptotically reaching those provided by the Singleton bound. The first
construction gives a family of Reed-Solomon codes with insdel error-correcting
capability asymptotic to its length. The second construction provides a family
of Reed Solomon codes with an exact insdel error-correcting capability up to
its length. Both our constructions improve the previously known construction of
2-dimensional Reed-Solomon codes whose insdel error-correcting capability is
only logarithmic on the code length.
