论文标题
MDS多吐线的芦苇 - 固体代码具有小尺寸船体
MDS multi-twisted Reed-Solomon codes with small dimensional hull
论文作者
论文摘要
在本文中，我们发现多吐芦苇固体代码为MD的必要条件。特别是，我们介绍了一类新的MDS twist twist的芦苇 - 溶解代码$ \ Mathcal {c} _ {\bmα，\ bm t，\ bm t，\ bm h，\ bm h，\ bm h，\bmη} $，带有Twists $ \ bm t =（1，2）$ and Hooks $ \ bm H =（bm H =（bm H =（0，1） $ \ mathbb {f} _q $，在$ \ mathbb {f} _ {16} $上提供一个非平凡的示例，并在大小的有限字段上进行枚举。因此，我们得出了具有小尺寸船体的MDS多扭静脉 - 固体代码的条件。
In this paper, we find a necessary and sufficient condition for multi-twisted Reed-Solomon codes to be MDS. In particular, we introduce a new class of MDS double-twisted Reed-Solomon codes $\mathcal{C}_{\bm α, \bm t, \bm h, \bm η}$ with twists $\bm t = (1, 2)$ and hooks $\bm h = (0, 1)$ over the finite field $\mathbb{F}_q$, providing a non-trivial example over $\mathbb{F}_{16}$ and enumeration over the finite fields of size up to 17. Moreover, we obtain necessary conditions for the existence of multi-twisted Reed-Solomon codes with small dimensional hull. Consequently, we derive conditions for the existence of MDS multi-twisted Reed-Solomon codes with small dimensional hull.
