论文标题
在带有任意维度的Galois船体的MDS代码上
On MDS Codes With Galois Hulls of Arbitrary Dimensions
论文作者
论文摘要
线性代码的GALOIS船体是线性代码的欧几里得和遗传学船体的概括。在本文中，我们研究了（扩展）GRS代码的Galois船体，并通过（扩展）GRS代码与任意维度的Galois Hulls呈现MDS代码的几个新结构。给出了两种用Hermitian或Garois Galois自动式（扩展）GRS代码构建MDS代码的MDS代码的通用方法。使用这些方法，可以获得一些具有较大维度的MDS代码和任意维度的Galois船体，并且相对严格的条件也可以导致许多新的MDS代码，其中具有任意维度的Galois船体。
The Galois hulls of linear codes are a generalization of the Euclidean and Hermitian hulls of linear codes. In this paper, we study the Galois hulls of (extended) GRS codes and present several new constructions of MDS codes with Galois hulls of arbitrary dimensions via (extended) GRS codes. Two general methods of constructing MDS codes with Galois hulls of arbitrary dimensions by Hermitian or general Galois self-orthogonal (extended) GRS codes are given. Using these methods, some MDS codes with larger dimensions and Galois hulls of arbitrary dimensions can be obtained and relatively strict conditions can also lead to many new classes of MDS codes with Galois hulls of arbitrary dimensions.
