On sets of subspaces with two intersection dimensions and a geometrical junta bound
Combinatorics
2021-08-09 v3
Abstract
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.
Cite
@article{arxiv.2009.06792,
title = {On sets of subspaces with two intersection dimensions and a geometrical junta bound},
author = {Giovanni Longobardi and Leo Storme and Rocco Trombetti},
journal= {arXiv preprint arXiv:2009.06792},
year = {2021}
}