In this paper, we provide conditions that hulls of generalized Reed-Solomon (GRS) codes are also GRS codes from algebraic geometry codes. If the conditions are not satisfied, we provide a method of linear algebra to find the bases of hulls of GRS codes and give formulas to compute their dimensions. Besides, we explain that the conditions are too good to be improved by some examples. Moreover, we show self-orthogonal and self-dual GRS codes.

翻译：本文给出了广义Reed-Solomon（GRS）码的包络同时也是代数几何码中的GRS码的条件。若不满足这些条件，我们提出了一种线性代数方法，用以寻找GRS码包络的基，并给出了计算其维数的公式。此外，通过若干实例说明这些条件已臻于完善而无法进一步改进。同时，我们展示了自正交和自对偶GRS码。