论文标题
最佳距离标志代码通过图表中的完美匹配来扩展
Optimum Distance Flag Codes from Spreads via Perfect Matchings in Graphs
论文作者
论文摘要
在本文中，我们在矢量空间上研究标志代码$ \ mathbb {f} _q^n $，是$ q $ a Prime Power和$ \ Mathbb {f} _Q $ $ q $元素的有限字段。更确切地说，我们专注于达到最大可能距离（最佳距离标志代码）的标志代码，并且可以从$ \ Mathbb {f} _Q^n $的差价中获得。我们表征了该国旗代码系列的一组可接受类型的向量，并根据有关图形中完美匹配的众所周知的结果提供了它们的结构。该构造既达到其类型向量的最大距离，也达到了该距离的最大可能的基数。
In this paper, we study flag codes on the vector space $\mathbb{F}_q^n$, being $q$ a prime power and $\mathbb{F}_q$ the finite field of $q$ elements. More precisely, we focus on flag codes that attain the maximum possible distance (optimum distance flag codes) and can be obtained from a spread of $\mathbb{F}_q^n$. We characterize the set of admissible type vectors for this family of flag codes and also provide a construction of them based on well-known results about perfect matchings in graphs. This construction attains both the maximum distance for its type vector and the largest possible cardinality for that distance.
