Coded caching systems have been widely studied to reduce the data transmission during the peak traffic time. In practice, two important parameters of a coded caching system should be considered, i.e., the rate which is the maximum amount of the data transmission during the peak traffic time, and the subpacketization level, the number of divided packets of each file when we implement a coded caching scheme. We prefer to design a scheme with rate and packet number as small as possible since they reflect the transmission efficiency and complexity of the caching scheme, respectively. In this paper, we first characterize a coded caching scheme from the viewpoint of linear algebra and show that designing a linear coded caching scheme is equivalent to constructing three classes of matrices satisfying some rank conditions. Then based on the invariant linear subspaces and combinatorial design theory, several classes of new coded caching schemes over $\mathbb{F}_2$ are obtained by constructing these three classes of matrices. It turns out that the rate of our new rate is the same as the scheme construct by Yan et al. (IEEE Trans. Inf. Theory 63, 5821-5833, 2017), but the packet number is significantly reduced. A concatenating construction then is used for flexible number of users. Finally by means of these matrices, we show that the minimum storage regenerating codes can also be used to construct coded caching schemes.

中文翻译：

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集中式网络的线性编码缓存方案

编码缓存系统已被广泛研究以减少高峰流量期间的数据传输。在实际应用中，编码缓存系统需要考虑两个重要参数，即流量高峰时段最大数据传输量的速率，以及子包化级别，实现时每个文件的分包数编码缓存方案。我们更喜欢设计一个速率和数据包数量尽可能小的方案，因为它们分别反映了缓存方案的传输效率和复杂度。在本文中，我们首先从线性代数的角度描述编码缓存方案，并表明设计线性编码缓存方案等效于构造满足某些秩条件的三类矩阵。然后基于不变线性子空间和组合设计理论，通过构造这三类矩阵，得到了$\mathbb{F}_2$上的几类新的编码缓存方案。事实证明，我们的新利率的利率与 Yan 等人的方案构造相同。(IEEE Trans. Inf. Theory 63, 5821-5833, 2017)，但包数明显减少。连接结构然后用于灵活数量的用户。最后通过这些矩阵，我们表明最小存储再生代码也可以用于构建编码缓存方案。事实证明，我们的新利率的利率与 Yan 等人的方案构造相同。(IEEE Trans. Inf. Theory 63, 5821-5833, 2017)，但包数明显减少。连接结构然后用于灵活数量的用户。最后通过这些矩阵，我们表明最小存储再生代码也可以用于构建编码缓存方案。事实证明，我们的新利率的利率与 Yan 等人的方案构造相同。(IEEE Trans. Inf. Theory 63, 5821-5833, 2017)，但包数明显减少。连接结构然后用于灵活数量的用户。最后通过这些矩阵，我们表明最小存储再生代码也可以用于构建编码缓存方案。