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
收藏
页码：323 / 340
页数：18
相关论文
共 50 条
  • [21] The List Decoding Radius of Reed-Muller Codes over Small Fields
    Bhowmick, Abhishek
    Lovett, Shachar
    STOC'15: PROCEEDINGS OF THE 2015 ACM SYMPOSIUM ON THEORY OF COMPUTING, 2015, : 277 - 285
  • [22] List Decoding of Reed-Muller Codes Based on a Generalized Plotkin Construction
    Yasunaga, Kenji
    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2013, E96A (07) : 1662 - 1666
  • [23] Weight Distribution and List-Decoding Size of Reed-Muller Codes
    Kaufman, Tali
    Lovett, Shachar
    Porat, Ely
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2012, 58 (05) : 2689 - 2696
  • [24] The List Decoding Radius for Reed-Muller Codes Over Small Fields
    Bhowmick, Abhishek
    Lovett, Shachar
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2018, 64 (06) : 4382 - 4391
  • [25] Approximate Local Decoding of Cubic Reed-Muller Codes Beyond the List Decoding Radius
    Hatami, Pooya
    Tulsiani, Madhur
    SODA'18: PROCEEDINGS OF THE TWENTY-NINTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2018, : 663 - 679
  • [26] Soft-decision list decoding of Reed-Muller codes with linear complexity
    Dumer, Ilya
    Kabatiansky, Grigory
    Tavernier, Cedric
    2011 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT), 2011,
  • [27] Soft-decision list decoding with linear complexity for the first-order Reed-Muller codes
    Dumer, Ilya
    Kabatiansky, Grigory
    Tavernier, Cedric
    2007 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-7, 2007, : 1346 - +
  • [28] Adaptive Viterbi Decoding of Reed-Muller Codes
    Mahran, Ashraf M.
    Magdy, Ahmed
    Elghandour, Ahmed
    2017 12TH INTERNATIONAL CONFERENCE ON COMPUTER ENGINEERING AND SYSTEMS (ICCES), 2017, : 314 - 319
  • [29] Automorphism Ensemble Decoding of Reed-Muller Codes
    Geiselhart, Marvin
    Elkelesh, Ahmed
    Ebada, Moustafa
    Cammerer, Sebastian
    ten Brink, Stephan
    IEEE TRANSACTIONS ON COMMUNICATIONS, 2021, 69 (10) : 6424 - 6438
  • [30] Multidimensional second order Reed-Muller codes as Grassmannian packings
    Ashikhmmin, Alexei
    Calderbank, A. Robert
    Kewlin, Wjatscheslaw
    2006 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1-6, PROCEEDINGS, 2006, : 1001 - 1005
12345