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List-Decoding Barnes-Wall Lattices.

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Název: List-Decoding Barnes-Wall Lattices.
Autoři: Grigorescu, Elena, Peikert, Chris
Zdroj: Computational Complexity; Jun2017, Vol. 26 Issue 2, p365-392, 28p
Abstrakt: The question of list-decoding error-correcting codes over finite fields (under the Hamming metric) has been widely studied in recent years. Motivated by the similar discrete linear structure of linear codes and point lattices in $${\mathbb{R}^{N}}$$ , and their many shared applications across complexity theory, cryptography, and coding theory, we initiate the study of list decoding for lattices. Namely: for a lattice $${\mathcal{L}\subseteq \mathbb{R}^N}$$ , given a target vector $${r \in \mathbb{R}^N}$$ and a distance parameter d, output the set of all lattice points $${w \in \mathcal{L}}$$ that are within distance d of r. In this work, we focus on combinatorial and algorithmic questions related to list decoding for the well-studied family of Barnes-Wall lattices. Our main contributions are twofold: [ABSTRACT FROM AUTHOR]
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Databáze: Complementary Index
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Abstrakt:The question of list-decoding error-correcting codes over finite fields (under the Hamming metric) has been widely studied in recent years. Motivated by the similar discrete linear structure of linear codes and point lattices in $${\mathbb{R}^{N}}$$ , and their many shared applications across complexity theory, cryptography, and coding theory, we initiate the study of list decoding for lattices. Namely: for a lattice $${\mathcal{L}\subseteq \mathbb{R}^N}$$ , given a target vector $${r \in \mathbb{R}^N}$$ and a distance parameter d, output the set of all lattice points $${w \in \mathcal{L}}$$ that are within distance d of r. In this work, we focus on combinatorial and algorithmic questions related to list decoding for the well-studied family of Barnes-Wall lattices. Our main contributions are twofold: [ABSTRACT FROM AUTHOR]
ISSN:10163328
DOI:10.1007/s00037-016-0151-x