论文标题
在具有两个相交维度和几何术语结合的子空间集
On sets of subspaces with two intersection dimensions and a geometrical junta bound
论文作者
论文摘要
在本文中，考虑了在规定的整数集中具有子空间距离的恒定尺寸子空间代码。这种对象的最简单示例是{\ it junta};即所有代码字可以通过共同子空间的子空间代码。我们专注于仅分配两个相交值的情况。在这种情况下，我们确定了由非junta代码元素跨越的向量空间维度的上限。此外，如果两个交叉值是连续的，我们证明这种界限很紧，并将获得最大维度的示例分类为四个无限家族之一。
In this article, constant dimension subspace codes whose codewords have subspace distance in a prescribed set of integers, are considered. The easiest example of such an object is a {\it junta}; i.e. a subspace code in which all codewords go through a common subspace. We focus on the case when only two intersection values for the codewords, are assigned. In such a case we determine an upper bound for the dimension of the vector space spanned by the elements of a non-junta code. In addition, if the two intersection values are consecutive, we prove that such a bound is tight, and classify the examples attaining the largest possible dimension as one of four infinite families.
