In this paper, we propose a mechanism for the construction of MDS codes with arbitrary dimensions of Euclidean hulls. Precisely, we construct (extended) generalized Reed-Solomon (GRS) codes with assigned dimensions of Euclidean hulls from self-orthogonal GRS codes. It turns out our constructions are more general than previous works on Euclidean hulls of (extended) GRS codes.

中文翻译：

---

关于MDS代码的欧氏壳

在本文中，我们提出了一种构造具有任意尺寸欧几里德船体的MDS代码的机制。精确地，我们根据自正交GRS代码构造（扩展）了具有指定欧几里得船体尺寸的广义Reed-Solomon（GRS）代码。事实证明，我们的构造比以前关于（扩展的）GRS代码的欧几里得船体的构造更具通用性。