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A construction of Abelian non-cyclic orbit codes

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Abstract

A constant dimension code consists of a set of k-dimensional subspaces of \(\mathbb {F}_{q}^{n}\), where \(\mathbb {F}_{q}\) is a finite field of q elements. Orbit codes are constant dimension codes which are defined as orbits under the action of a subgroup of the general linear group on the set of all k-dimensional subspaces of \(\mathbb {F}_{q}^{n}\). If the acting group is Abelian, we call the corresponding orbit code Abelian orbit code. In this paper we present a construction of an Abelian non-cyclic orbit code for which we compute its cardinality and its minimum subspace distance. Our code is a partial spread and consequently its minimum subspace distance is maximal.

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Acknowledgments

This work was partially supported by Spanish grants AICO/2017/128 of the Generalitat Valenciana and VIGROB287 of the Universitat d’Alacant.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat d’Alacant, Ap. Correus 99, E-03080, Alacant, Spain

    Joan-Josep Climent, Verónica Requena & Xaro Soler-Escrivà

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  1. Joan-Josep Climent
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  2. Verónica Requena
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  3. Xaro Soler-Escrivà
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Correspondence to Joan-Josep Climent.

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This article is part of the Topical Collection on Special Issue on Coding Theory and Applications

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Climent, JJ., Requena, V. & Soler-Escrivà, X. A construction of Abelian non-cyclic orbit codes. Cryptogr. Commun. 11, 839–852 (2019). https://doi.org/10.1007/s12095-018-0306-5

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