An algorithm for list decoding number field codes

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 [1] and Guruswami [2]. 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 [3] where O_K is the ring of integers of a number field K.