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Support Constrained Generator Matrices of Gabidulin Codes in Characteristic Zero

Yildiz, Hikmet and Raviv, Netanel and Hassibi, Babak (2020) Support Constrained Generator Matrices of Gabidulin Codes in Characteristic Zero. In: 2020 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 60-65. ISBN 978-1-7281-6432-8. https://resolver.caltech.edu/CaltechAUTHORS:20200526-154649443

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Abstract

Gabidulin codes over fields of characteristic zero were recently constructed by Augot et al., whenever the Galois group of the underlying field extension is cyclic. In parallel, the interest in sparse generator matrices of Reed–Solomon and Gabidulin codes has increased lately, due to applications in distributed computations. In particular, a certain condition pertaining to the intersection of zero entries at different rows, was shown to be necessary and sufficient for the existence of the sparsest possible generator matrix of Gabidulin codes over finite fields. In this paper we complete the picture by showing that the same condition is also necessary and sufficient for Gabidulin codes over fields of characteristic zero.Our proof builds upon and extends tools from the finite-field case, combines them with a variant of the Schwartz–Zippel lemma over automorphisms, and provides a simple randomized construction algorithm whose probability of success can be arbitrarily close to one. In addition, potential applications for low-rank matrix recovery are discussed.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT44484.2020.9174524DOIArticle
https://arxiv.org/abs/2004.14430arXivDiscussion Paper
ORCID:
AuthorORCID
Yildiz, Hikmet0000-0002-0891-3352
Raviv, Netanel0000-0002-1686-1994
Additional Information:© 2020 IEEE.
Record Number:CaltechAUTHORS:20200526-154649443
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200526-154649443
Official Citation:H. Yildiz, N. Raviv and B. Hassibi, "Support Constrained Generator Matrices of Gabidulin Codes in Characteristic Zero," 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 2020, pp. 60-65, doi: 10.1109/ISIT44484.2020.9174524
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103479
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 May 2020 22:49
Last Modified:28 Aug 2020 21:22

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