论文标题
最佳距离旗代码的轨道结构
An Orbital Construction of Optimum Distance Flag Codes
论文作者
论文摘要
标志代码是由矢量空间$ \ mathbb {f} _q^n $的嵌套子空间（flags）序列组成的多疗法网络代码，其中$ q $是主要功率，$ \ m athbb {f} _q $，大小$ q $的有限字段。在本文中，我们研究了$ \ mathbb {f} _q^{2k} $上的完整标志代码的构造，该代码具有最大距离（最佳距离完整标志代码），这些代码可以赋予由通用线性组的子组的作用提供的轨道结构。更确切地说，从尺寸$ K $的子空间代码开始，并具有给定的轨道描述的最大距离，我们提供了足够的条件，以获取$ \ Mathbb {f} _Q^{2K} $具有最佳距离完整标志代码，其轨道结构直接直接引起了前一个。特别是，我们表现出一种特定的轨道结构，具有最佳尺寸的特定尺寸，这是由于平面在$ \ mathbb {f} _q^{2k} $上扩散的轨道结构，这在很大程度上取决于该领域的特征。
Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space $\mathbb{F}_q^n$, where $q$ is a prime power and $\mathbb{F}_q$, the finite field of size $q$. In this paper we study the construction on $\mathbb{F}_q^{2k}$ of full flag codes having maximum distance (optimum distance full flag codes) that can be endowed with an orbital structure provided by the action of a subgroup of the general linear group. More precisely, starting from a subspace code of dimension $k$ and maximum distance with a given orbital description, we provide sufficient conditions to get an optimum distance full flag code on $\mathbb{F}_q^{2k}$ having an orbital structure directly induced by the previous one. In particular, we exhibit a specific orbital construction with the best possible size from an orbital construction of a planar spread on $\mathbb{F}_q^{2k}$ that strongly depends on the characteristic of the field.
