论文标题
网络编码中平面物的标志代码
Flag Codes from Planar Spreads in Network Coding
论文作者
论文摘要
在本文中，我们研究了一类由矢量空间$ \ mathbb {f} _q^n $的嵌套子空间（flags）给出的多疗法网络代码，是$ q $ a Prime Power和$ \ Mathbb {f} _Q $ $ Q $元素的有限领域。特别是，我们专注于具有最大最小距离的标志代码（最佳距离标志代码）。我们根据后者的良好特性探索这些代码的存在。对于$ n = 2k $，我们表明最佳距离尺寸最大的距离完全旗代码正是可以从平面传播构建的最佳距离代码。我们提供了它们的精确构造以及解码算法。
In this paper we study a class of multishot network codes given by families of nested subspaces (flags) of a vector space $\mathbb{F}_q^n$, being $q$ a prime power and $\mathbb{F}_q$ the finite field of $q$ elements. In particular, we focus on flag codes having maximum minimum distance (optimum distance flag codes). We explore the existence of these codes from spreads, based on the good properties of the latter ones. For $n=2k$, we show that optimum distance full flag codes with the largest size are exactly those that can be constructed from a planar spread. We give a precise construction of them as well as a decoding algorithm.
