Abstract
Given a finite field \(\mathbb {F}_{q}\), a constant dimension code is a set of k-dimensional subspaces of \(\mathbb {F}_{q}^{n}\). Orbit codes are constant dimension codes which are defined as orbits when the action of a subgroup of the general linear group on the set of all subspaces of \(\mathbb {F}_{q}^{n}\) is considered. In this paper we present a construction of an Abelian non-cyclic orbit code whose minimum subspace distance is maximal.
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Acknowledgements
The first author was supported by grants MIMECO MTM2015-68805-REDT and MTM2015-69138-REDT.
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Climent, JJ., Requena, V., Soler-Escrivà, X. (2017). A Construction of Orbit Codes. In: Barbero, Á., Skachek, V., Ytrehus, Ø. (eds) Coding Theory and Applications. ICMCTA 2017. Lecture Notes in Computer Science(), vol 10495. Springer, Cham. https://doi.org/10.1007/978-3-319-66278-7_7
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DOI: https://doi.org/10.1007/978-3-319-66278-7_7
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