An improved list decoding algorithm for the second order Reed-Muller codes and its applications

被引：22

作者：

Fourquet, Rafael ^{[1
]}

Tavernier, Cedric ^{[2
]}

机构：

[1] Univ Paris 8 St Denis MAATICAH, Dept Math, F-93526 St Denis, France

[2] THALES Commun, Colombes, France

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2008年 / 49卷 / 1-3期

关键词：

list decoding; Reed-Muller codes; covering radius; Boolean functions; cryptography;

D O I：

10.1007/s10623-008-9184-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We propose an algorithm which is an improved version of the Kabatiansky-Tavernier list decoding algorithm for the second order Reed-Muller code RM(2, m), of length n = 2(m), and we analyse its theoretical and practical complexity. This improvement allows a better theoretical complexity. Moreover, we conjecture another complexity which corresponds to the results of our simulations. This algorithm has the strong property of being deterministic and this fact drives us to consider some applications, like determining some lower bounds concerning the covering radius of the RM(2, m) code.

引用

页码：323 / 340

页数：18

共 50 条

[31] Sequential decoding of binary Reed-Muller codes
Stolte, Norbert
Sorger, Ulrich
AEU-Archiv fur Elektronik und Ubertragungstechnik, 2000, 54 (06): : 412 - 420
[32] The optimum distance profiles of the second order Reed-Muller codes
Chen, Yanling
Vinck, A. J. Han
2009 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1- 4, 2009, : 2236 - +
[33] Permutation decoding of first-order Generalized Reed-Muller codes
Bernal, Jose Joaquin
Simon, Juan Jacobo
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2025,
[34] Simple MAP decoding of first order Reed-Muller and hamming codes
Ashikhmin, A
Litsyn, S
2003 IEEE INFORMATION THEORY WORKSHOP, PROCEEDINGS, 2003, : 18 - 21
[35] Simple MAP decoding of first order Reed-Muller and hamming codes
Ashikhmin, A
Litsyn, S
22ND CONVENTION OF ELECTRICAL AND ELECTRONICS ENGINEERS IN ISRAEL, PROCEEDINGS, 2002, : 141 - 143
[36] Recursive and permutation decoding for Reed-Muller codes
Dumer, I
Shabunov, K
ISIT: 2002 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2002, : 146 - 146
[37] Partial permutation decoding for the first-order Reed-Muller codes
Seneviratne, P.
DISCRETE MATHEMATICS, 2009, 309 (08) : 1967 - 1970
[38] Sequential decoding of binary Reed-Muller codes
Stolte, N
Sorger, U
AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS, 2000, 54 (06) : 412 - 420
[39] On polylogarithmic decoding complexity for Reed-Muller codes
Dumer, I
2004 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2004, : 326 - 326
[40] DECODING REED-MULLER CODES BY MULTILAYER PERCEPTRONS
TSENG, YH
WU, JL
INTERNATIONAL JOURNAL OF ELECTRONICS, 1993, 75 (04) : 589 - 594

← 1 2 3 4 5 →