论文标题
多层结构的界限
Bounds for the multilevel construction
论文作者
论文摘要
随机网络编码的主要问题之一是在投影空间中所谓的子空间代码$ \ Mathcal {p} _q（n）$中，在给定的最低距离的最低距离上计算出良好的下限和上限。确定确切的最大基数的确定是一个非常困难的离散优化问题，涉及大量对称性。除了\ textit {good}子空间代码的一些显式结构外，最成功的完整构造涉及离散优化子问题本身的解决方案，这些解决方案本身并未系统地解决。在这里，我们考虑了多级又称\ echelon- fefrers的构造，并为可实现的红衣主教提供了下限和上限。从更一般的角度来看，我们在加权图中解决了最大的集团问题，其中权重可以是字段尺寸$ q $中的多项式。
One of the main problems in random network coding is to compute good lower and upper bounds on the achievable cardinality of the so-called subspace codes in the projective space $\mathcal{P}_q(n)$ for a given minimum distance. The determination of the exact maximum cardinality is a very tough discrete optimization problem involving a huge number of symmetries. Besides some explicit constructions for \textit{good} subspace codes several of the most success full constructions involve the solution of discrete optimization subproblems itself, which mostly have not been not been solved systematically. Here we consider the multilevel a.k.a.\ Echelon--Ferrers construction and given lower and upper bounds for the achievable cardinalities. From a more general point of view, we solve maximum clique problems in weighted graphs, where the weights can be polynomials in the field size $q$.
