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An algorithm for list decoding number field codes

Abstract : We present an algorithm for list decoding codewords of algebraic number field codes in polynomial time. This is the first explicit procedure for decoding number field codes whose construction were previously described by Lenstra and Guruswami. We rely on a new algorithm for computing the Hermite normal form of the basis of an $O_K$-module due to Biasse and Fieker where $O_K$ is the ring of integers of a number field K.
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https://hal.inria.fr/hal-01113662
Contributor : Daniel Augot <>
Submitted on : Friday, February 6, 2015 - 9:48:49 AM
Last modification on : Saturday, May 1, 2021 - 3:40:59 AM

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Guillaume Quintin, Jean-François Biasse. An algorithm for list decoding number field codes. 2012 IEEE International Symposium on Information Theory (ISIT 2012), Jul 2012, Cambridge, United States. pp.91-95, ⟨10.1109/ISIT.2012.6284696⟩. ⟨hal-01113662⟩

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