# American Institute of Mathematical Sciences

August  2016, 10(3): 633-642. doi: 10.3934/amc.2016031

## On self-dual MRD codes

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

Received  May 2015 Revised  December 2015 Published  August 2016

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 $(\mathbb{F}_q)^{n\times n}$.
Citation: Gabriele Nebe, Wolfgang Willems. On self-dual MRD codes. Advances in Mathematics of Communications, 2016, 10 (3) : 633-642. doi: 10.3934/amc.2016031
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