论文标题
MDS线性代码具有一维船体
MDS linear codes with one dimensional hull
论文作者
论文摘要
我们将线性代码$ c $的欧几里得船体定义为$ c $的交叉点及其欧几里得双$ c^\ perp $。由于其在确定算法的复杂性来计算线性代码的自动形态组并检查两个线性代码的置换等效性方面，因此具有较低维度的船体引起了人们的兴趣。最近已证明，任何$ q $ -ary $ [n，k] $ q> 3 $线性代码产生具有相同参数的线性代码，并且具有零维欧几里得船体，该代码称为线性互补的双代码。本文旨在探索具有一维欧几里得船体的MDS线性代码家族的明确结构。我们获得了几类此类代码。
We define the Euclidean hull of a linear code $C$ as the intersection of $C$ and its Euclidean dual $C^\perp$. The hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing the automorphism group of a linear code and checking permutation equivalence of two linear codes. It has been recently proved that any $q$-ary $[n,k]$ linear code with $q>3$ gives rise to a linear code with the same parameters and having zero dimensional Euclidean hull, which is known as a linear complementary dual code. This paper aims to explore explicit constructions of families of MDS linear codes with one dimensional Euclidean hull. We obtain several classes of such codes.
