Dimensions of the hull of generalized Reed-Solomon codes - Huang, Jing; Liu, Jingge; Yu, Dong (AIMS mathematics, 2024)
Let GRS$ _k(\boldsymbol{α}, \boldsymbol{υ}) $ be a $ k $-dimensional generalized Reed-Solomon (GRS) code over $ \mathbb{F}_q $ associated with $ \boldsymbol{α} = (α_1, …, α_n) $ and $ \boldsymbol{υ} = (υ_1, …, υ_n) $. In this paper, we determined the dimension of the Euclidean hull GRS$ _k(\boldsymbol{α}, \boldsymbol{υ})\; \cap $ GRS$ _k(\boldsymbol{α}, \boldsymbol{υ})^\bot $, which addresses an open problem posed in [Chen et al., IEEE-TIT, 2023]. We also presentd a new approach to generating all self-dual RS codes.