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Paper IDA.2.5
Paper Title Support Constrained Generator Matrices of Gabidulin Codes in Characteristic Zero
Authors Hikmet Yildiz, California Institute of Technology, United States; Netanel Raviv, Washington University in Saint Louis, United States; Babak Hassibi, California Institute of Technology, United States
Session A.2: Algebraic Coding Theory II
Presentation Lecture
Track Algebraic and Combinatorial Coding Theory
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
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.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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