On primitive constant dimension codes and a geometrical sunflower bound

Roland D. Barrolleta; Emilio Suárez-Canedo; Leo Storme; Peter Vandendriessche

doi:10.3934/amc.2017055

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2017, Volume 11, Issue 4: 757-765. Doi: 10.3934/amc.2017055

This issue Previous Article On the classification of $\mathbb{Z}_4$-codes Next Article On the performance of optimal double circulant even codes

On primitive constant dimension codes and a geometrical sunflower bound

1.
Departament d'Enginyeria de la Informacio i de les Comunicacions, Edifici Q, Universitat Autónoma de Barcelona, 08193 -Bellaterra -Cerdanyola del Vallés (Barcelona), Spain
2.
Department of Mathematics (WE01), Krijgslaan 281 -building S25, 9000 Gent, Belgium

Received: April 2016

Published: July 2018

The fourth author is supported by a postdoctoral grant of the FWO-Flanders.

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Abstract

In this paper we study subspace codes with constant intersection dimension (SCIDs). We investigate the largest possible dimension spanned by such a code that can yield non-sunflower codes, and classify the examples attaining equality in that bound as one of two infinite families. We also construct a new infinite family of primitive SCIDs.

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Mathematics Subject Classification: 05B25, 51E20, 94B60.

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Figure 1. The $(k,k-t)$-SCID described in Example 1

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Figure 2. The $(k,k-t)$-SCID described in Example 2

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