List decoding of number field codes

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...

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Veröffentlicht in:	Designs, codes, and cryptography codes, and cryptography, 2014-09, Vol.72 (3), p.687-711
1. Verfasser:	Coxon, Nicholas
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Algorithmics. Computability. Computer arithmetics Applied sciences Circuits Coding and Information Theory Coding, codes Computer Science Computer science control theory systems Cryptology Data Structures and Information Theory Discrete Mathematics in Computer Science Exact sciences and technology Information and Communication Information Theory Information, signal and communications theory Mathematics Number theory Sciences and techniques of general use Signal and communications theory Symbolic Computation Telecommunications and information theory Theoretical computing
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Beschreibung
Zusammenfassung:	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.
ISSN:	0925-1022 1573-7586
DOI:	10.1007/s10623-013-9803-x