On self-dual MRD codes

Gabriele Nebe; Wolfgang  Willems

doi:10.3934/amc.2016031

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2016, Volume 10, Issue 3: 633-642. Doi: 10.3934/amc.2016031

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On self-dual MRD codes

Gabriele Nebe^1, and
Wolfgang Willems^2,

1.
Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen
2.
Fakultät für Mathematik, Otto-von-Guericke Universität, Magdeburg

Received: April 30, 2015

Revised: November 30, 2015

Published: July 2016

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Abstract

We investigate self-dual MRD codes. In particular we prove that a Gabidulin code in $(\mathbb{F}_q)^{n\times n}$ is equivalent to a self-dual code if and only if its dimension is $n^2/2$, $n \equiv 2 \pmod 4$, and $q \equiv 3 \pmod 4$. On the way we determine the full automorphism group of Gabidulin codes in $(\mathbb{F}_q)^{n\times n}$.

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Mathematics Subject Classification: Primary: 94B05; Secondary: 20B25.

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References

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