# A complete characterization of irreducible cyclic orbit codes

Trautmann, A L; Rosenthal, J (2011). A complete characterization of irreducible cyclic orbit codes. In: WCC 2011 - Seventh Workshop on Coding and Cryptography, Paris, FR, 11 April 2011 - 14 April 2011. HAL-Inria, 219-228.

## Abstract

Constant dimension codes are subsets of the nite Grassmann variety. The study of constant dimension codes with good distances have been central in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are characterized that the elements of the code can be viewed as the orbit under a group action. The paper gives a complete characterization of orbit codes that are generated by an irreducible cyclic group, i.e. an irreducible group having one generator. We show how some of the basic properties of these codes, the cardinality and the minimum distance, can be derived using the isomorphism of the vector space and the extension field.

## Abstract

Constant dimension codes are subsets of the nite Grassmann variety. The study of constant dimension codes with good distances have been central in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are characterized that the elements of the code can be viewed as the orbit under a group action. The paper gives a complete characterization of orbit codes that are generated by an irreducible cyclic group, i.e. an irreducible group having one generator. We show how some of the basic properties of these codes, the cardinality and the minimum distance, can be derived using the isomorphism of the vector space and the extension field.

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Item Type: Conference or Workshop Item (Other), not_refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 14 April 2011 23 Feb 2012 21:18 03 Aug 2021 15:16 HAL-Inria Proceedings of the ... International Workshop on Coding and Cryptography 7 Green http://hal.inria.fr/inria-00611789 http://arxiv.org/abs/1102.3167http://wcc2011.inria.fr/ (Organisation)