Optimal RS Codes and GRS Codes Against Adversarial Insertions and Deletions and Optimal Constructions
Jingge Liu · IEEE Transactions on Information Theory · 2024
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.