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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, 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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Additional indexing

Item Type:Conference or Workshop Item (Other), not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Event End Date:14 April 2011
Deposited On:23 Feb 2012 21:18
Last Modified:21 Nov 2017 15:57
Publisher:HAL-Inria
Series Name:Proceedings of the ... International Workshop on Coding and Cryptography
Number:7
Official URL:http://hal.inria.fr/inria-00611789
Related URLs:http://arxiv.org/abs/1102.3167
http://wcc2011.inria.fr/ (Organisation)

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