Optimal subspace codes in $ {{\rm{PG}}}(4,q) $

Antonio Cossidente; Francesco Pavese; Leo Storme

doi:10.3934/amc.2019025

Article Contents

2019, Volume 13, Issue 3: 393-404. Doi: 10.3934/amc.2019025

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Optimal subspace codes in $ {{\rm{PG}}}(4,q) $

1.
Department of Mathematics, Informatics and Economics, University of Basilicata, Contrada Macchia Romana, 85100 Potenza, Italy
2.
Dipartimento di Mechanics, Mathematics and Management, Polytechnic University of Bari, Via Orabona 4, 70125 Bari, Italy
3.
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281 - Building S8, 9000 Ghent, Belgium

^* Corresponding author
^* Corresponding author

Received: June 30, 2017

Revised: May 31, 2018

Published: August 2019

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Abstract

We investigate subspace codes whose codewords are subspaces of ${\rm{PG}}(4,q)$ having non-constant dimension. In particular, examples of optimal mixed-dimension subspace codes are provided, showing that $\mathcal{A}_q(5,3) = 2(q^3+1)$.

Keywords:

Galois geometry,
subspace codes.

Mathematics Subject Classification: Primary: 05B25; Secondary: 51E20, 94B25.

Citation:

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Figure 1. Construction for $ q $ odd

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Figure 2. Construction for $ q $ even

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Figure 3. Construction in PG$ (5,q) $, $ q $ even

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Figure 4. Construction in the hyperplane $ S $ of PG$ (5,q) $, $ q $ even

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References

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