Optimal RS Codes and GRS Codes Against Adversarial Insertions and Deletions and Optimal Constructions

In this paper, we study the optimal RS codes and GRS codes with respect to the half-Singleton bound and the strict half-Singleton bound, respectively. We first provide an improved explicit construction of optimal RS codes that meet the half-Singleton bound. This explicit construction can obtain optimal RS codes of longer lengths than previous studies. Then we focus on the optimal GRS codes with respect to the strict half-Singleton bound. We prove the existence of such codes and provide an explicit construction of such codes over much larger fields.