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Cyclic orbit codes


Trautmann, Anna-Lena; Manganiello, Felice; Braun, Michael; Rosenthal, Joachim (2013). Cyclic orbit codes. IEEE Transactions on Information Theory, 59(11):7386-7404.

Abstract

A constant dimension code consists of a set of k-dimensional subspaces of Fqn. Orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group, acting on the set of all subspaces of Fqn. If the acting group is cyclic, the corresponding orbit codes are called cyclic orbit codes. In this paper, we show how orbit codes can be seen as an analog of linear codes in the block coding case. We investigate how the structure of cyclic orbit codes can be utilized to compute the minimum distance and cardinality of a given code and propose different decoding procedures for a particular subclass of cyclic orbit codes.

Abstract

A constant dimension code consists of a set of k-dimensional subspaces of Fqn. Orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group, acting on the set of all subspaces of Fqn. If the acting group is cyclic, the corresponding orbit codes are called cyclic orbit codes. In this paper, we show how orbit codes can be seen as an analog of linear codes in the block coding case. We investigate how the structure of cyclic orbit codes can be utilized to compute the minimum distance and cardinality of a given code and propose different decoding procedures for a particular subclass of cyclic orbit codes.

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15 citations in Web of Science®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2013
Deposited On:27 Dec 2013 12:58
Last Modified:05 Apr 2016 17:17
Publisher:Institute of Electrical and Electronics Engineers
ISSN:0018-9448
Publisher DOI:https://doi.org/10.1109/TIT.2013.2274266

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