标题： 关于实现$(r,l)$分数线性网络编码 显示英文标题

标题： On Achievability of an $(r,l)$ Fractional Linear Network Code

摘要： 已知存在一种称为M网络的网络，它不是标量线性可解的，但对于消息维度为二时具有向量线性解。最近，已经提出了一种该结果的推广，其中表明对于任何整数$m\geq 2$，存在一种网络，它具有$(m,m)$维向量线性解，但对于$w<m$不具有$(w,w)$维向量线性解。本文提出了进一步的推广。 具体来说，我们证明对于任何正整数$k,n,$和$m\geq 2$，都存在一个网络具有$(mk,mn)$分数线性解，但不具有$(wk,wn)$分数线性解，其中$w<m$。 显示英文摘要

摘要： It is known that there exists a network, called as the M-network, which is not scalar linearly solvable but has a vector linear solution for message dimension two. Recently, a generalization of this result has been presented where it has been shown that for any integer $m\geq 2$, there exists a network which has a $(m,m)$ vector linear solution, but does not have a $(w,w)$ vector linear solution for $w<m$. This paper presents a further generalization. Specifically, we show that for any positive integers $k,n,$ and $m\geq 2$, there exists a network which has a $(mk,mn)$ fractional linear solution, but does not have a $(wk,wn)$ fractional linear solution for $w<m$.