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On sets of subspaces with two intersection dimensions and a geometrical junta bound
Designs, Codes and Cryptography ( IF 1.6 ) Pub Date : 2021-10-19 , DOI: 10.1007/s10623-021-00931-2
Giovanni Longobardi 1 , Leo Storme 2 , Rocco Trombetti 3
Affiliation  

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 junta (Combin Probab Comput 18(1–2):107–122, 2009); 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.



中文翻译:

在具有两个相交维度和几何军政府边界的子空间集上

在本文中,考虑了其码字在规定的整数集合中具有子空间距离的恒定维子空间码。这种对象最简单的例子是军政府(Combin Probab Comput 18(1-2):107-122, 2009);即子空间代码,其中所有代码字都经过一个公共子空间。我们关注仅分配代码字的两个交集值的情况。在这种情况下,我们确定由非军政府代码的元素跨越的向量空间维度的上限。此外,如果两个交集值是连续的,我们证明这样的界限是紧的,并将达到最大可能维度的例子分类为四个无限家族之一。

更新日期:2021-10-21
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