List decoding of number field codes

被引：0
作者：
Nicholas Coxon
机构：
[1] The University of Queensland,School of Mathematics and Physics
来源：
Designs, Codes and Cryptography | 2014年 / 72卷
关键词：
Number field codes; Chinese remainder codes; List decoding; 11T71; 11H71; 11Y40;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：687 / 711
页数：24
相关论文
共 26 条
  • [1] Belabas K.(2004)A relative van Hoeij algorithm over number fields J. Symb. Comput. 37 641-668
  • [2] Belabas K.(2004)Topics in computational algebraic number theory J. Théor. Nr. Bordx. 16 19-63
  • [3] Boneh D.(2002)Finding smooth integers in short intervals using CRT decoding J. Comput. Syst. Sci. 64 768-784
  • [4] Forney G.D.(1966)Generalized minimum distance decoding IEEE Trans. Inf. Theory IT -12 125-131
  • [5] Goldreich O.(2000)Chinese remaindering with errors IEEE Trans. Inf. Theory 46 1330-1338
  • [6] Ron D.(2003)Constructions of codes from number fields IEEE Trans. Inf. Theory 49 594-603
  • [7] Sudan M.(1999)Improved decoding of Reed–Solomon and algebraic–geometry codes IEEE Trans. Inf. Theory 45 1757-1767
  • [8] Guruswami V.(1975)On computing the exact determinant of matrices with polynomial entries J. Assoc. Comput. Mach. 22 38-50
  • [9] Guruswami V.(1962)A new upper bound for error-correcting codes IRE Trans. IT -8 203-207
  • [10] Sudan M.(1963)Improved asymptotic bounds for error-correcting codes IEEE Trans. Inf. Theory IT -9 198-205
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