List decoding of number field codes

Nicholas Coxon (1)

1 GRACE - Geometry, arithmetic, algorithms, codes and encryption

This paper presents a list decoding algorithm for the number field codes of Guruswami (IEEE Trans Inf Theory 49:594–603, 2003). The algorithm is an implementation of the unified framework for list decoding of algebraic codes of Guruswami, Sahai and Sudan (Proceedings of the 41st Annual Symposium on Foundations of Computer Science, 2000), specialised for number field codes. The computational complexity of the algorithm is evaluated in terms of the size of the inputs and field invariants.

Mots clés: Number field codes; Chinese remainder codes; List decoding

Domaines: Calcul formel [cs.SC]; Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Nicholas Coxon. List decoding of number field codes. Designs, Codes and Cryptography, 2014, 72 (3), pp.687-711. ⟨10.1007/s10623-013-9803-x⟩. ⟨hal-01947490⟩