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Gabidulin Codes with Support Constraints

Yildiz, Hikmet and Hassibi, Babak (2019) Gabidulin Codes with Support Constraints. In: 2019 IEEE Information Theory Workshop (ITW). IEEE , Piscataway, NJ, pp. 1-5. ISBN 978-1-5386-6900-6. https://resolver.caltech.edu/CaltechAUTHORS:20200214-103053761

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Abstract

Gabidulin codes are the first general construction of linear codes that are maximum rank distance (MRD). They have found applications in linear network coding, for example, when the transmitter and receiver are oblivious to the inner workings and topology of the network (the so-called incoherent regime). The reason is that Gabidulin codes can be used to map information to linear subspaces, which in the absence of errors cannot be altered by linear operations, and in the presence of errors can be corrected if the subspace is perturbed by a small rank. Furthermore, in distributed coding and distributed systems, one is led to the design of error correcting codes whose generator matrix must satisfy a given support constraint. In this paper, we give necessary and sufficient conditions on the support of the generator matrix that guarantees the existence of Gabidulin codes and general MRD codes. When the rate of the code is not very high, this is achieved with the same field size necessary for Gabidulin codes with no support constraint. When these conditions are not satisfied, we characterize the largest possible rank distance under the support constraints and show that they can be achieved by subcodes of Gabidulin codes. The necessary and sufficient conditions are identical to those that appear for MDS codes which were recently proven in [1], [2] in the context of settling the GM-MDS conjecture.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ITW44776.2019.8988992DOIArticle
https://arxiv.org/abs/1903.09360arXivDiscussion Paper
ORCID:
AuthorORCID
Yildiz, Hikmet0000-0002-0891-3352
Alternate Title:Gabidulin Codes with Support Constrained Generator Matrices
Additional Information:© 2019 IEEE.
Subject Keywords:Gabidulin codes, rank distance
Record Number:CaltechAUTHORS:20200214-103053761
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200214-103053761
Official Citation:H. Yildiz and B. Hassibi, "Gabidulin Codes with Support Constraints," 2019 IEEE Information Theory Workshop (ITW), Visby, Sweden, 2019, pp. 1-5. doi: 10.1109/ITW44776.2019.8988992
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101292
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Feb 2020 18:39
Last Modified:14 Feb 2020 18:39

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