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arXiv · 2009.06792

On sets of subspaces with two intersection dimensions and a geometrical junta bound

Giovanni Longobardi·Leo Storme·Rocco Trombetti
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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.

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Giovanni Longobardi, Leo Storme, Rocco Trombetti. 2021-08-06. On sets of subspaces with two intersection dimensions and a geometrical junta bound. https://arxiv.org/abs/2009.06792

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