Algebraic structures of MRD codes

Javier de la  Cruz; Michael Kiermaier; Alfred Wassermann; Wolfgang Willems

doi:10.3934/amc.2016021

Article Contents

2016, Volume 10, Issue 3: 499-510. Doi: 10.3934/amc.2016021

This issue Previous Article Further results on the classification of MDS codes Next Article Construction of 3-designs using $(1,\sigma)$-resolution

Algebraic structures of MRD codes

1.
Departamento de Matemáticas, Universidad del Norte, Km 5 Vía Puerto Colombia, Barranquilla
2.
Institut für Mathematik, Universität Bayreuth, 95440 Bayreuth
3.
Department of Mathematics, University of Bayreuth, 95440 Bayreuth
4.
Department of Mathematics, Otto-von-Guericke-University, 39016 Magdeburg

Received: March 31, 2015

Revised: March 31, 2016

Published: July 2016

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Abstract

Based on results in finite geometry we prove the existence of MRD codes in $(\mathbb{F}_q)_{n,n}$ with minimum distance $n$ which are essentially different from Gabidulin codes. The construction results from algebraic structures which are closely related to those of finite fields. Some of the results may be known to experts, but to our knowledge have never been pointed out explicitly in the literature.

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Mathematics Subject Classification: Primary: 94B99, 16Y60; Secondary: 15B33.

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