论文标题
涵盖格拉斯曼尼亚法规：界限和建筑
Covering Grassmannian Codes: Bounds and Constructions
论文作者
论文摘要
Grassmannian $ \ MATHCAL {G} _Q（n，k）$是矢量空间的所有$ k $维二维子空间的集合，最近，Etzion和Zhang在网络编码网络中用于网络编码式网络，最近将新的诺斯求婚用于覆盖Grassmannian代码。 $α$ - $（n，k，δ）_q^c $覆盖Grassmannian代码$ \ MATHCAL {C} $是$ \ Mathcal {g} _q（n，k）的子集$ \ mathbb {f} _q^n。$在本文中，我们在覆盖Grassmannian代码的大小上得出了新的上和下限。这些边界改善并扩展了已知边界的参数范围。
Grassmannian $\mathcal{G}_q(n,k)$ is the set of all $k$-dimensional subspaces of the vector space $\mathbb{F}_q^n.$ Recently, Etzion and Zhang introduced a new notion called covering Grassmannian code which can be used in network coding solutions for generalized combination networks. An $α$-$(n,k,δ)_q^c$ covering Grassmannian code $\mathcal{C}$ is a subset of $\mathcal{G}_q(n,k)$ such that every set of $α$ codewords of $\mathcal{C}$ spans a subspace of dimension at least $δ+k$ in $\mathbb{F}_q^n.$ In this paper, we derive new upper and lower bounds on the size of covering Grassmannian codes. These bounds improve and extend the parameter range of known bounds.
