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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 OK-module due to Biasse and Fieker  where OK is the ring of integers of a number field K.
Date of Conference: 1-6 July 2012