ALGORITHMS FOR THE MINIMUM WEIGHT OF LINEAR CODES

被引：6
|
作者：
Lisonek, Petr [1 ]
Trummer, Layla [1 ]
机构：
[1] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2016年 / 10卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Linear code; minimum weight algorithm; Brouwer-Zimmermann algorithm; information set; matroid partition; DISTANCE;
D O I：
10.3934/amc.2016.10.195
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We outline the algorithm for computing the minimum weight of a linear code over a finite field that was invented by A. Brouwer and later extended by K.-H. Zimmermann. We show that matroid partitioning algorithms can be used to efficiently find a favourable (and sometimes best possible) sequence of information sets on which the Brouwer-Zimmermann algorithm operates. We present a new algorithm for computing the minimum weight of a linear code. We use a large set of codes to compare our new algorithm with the Brouwer-Zimmermann algorithm. We find that for about one third of codes in this sample set, our algorithm requires to generate fewer codewords than the Brouwer-Zimmermann algorithm.
引用
收藏
页码：195 / 207
页数：13
相关论文
共 50 条
  • [1] Minimum distance decoding algorithms for linear codes
    Barg, A
    APPLIED ALGEBRA, ALGEBRAIC ALGORITHMS AND ERROR-CORRECTING CODES, 1997, 1255 : 1 - 14
  • [2] Computation of Minimum Hamming Weight for Linear Codes
    Rostami, Esmaeil
    Nekooei, Reza
    IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS, 2019, 14 (01): : 81 - 93
  • [3] Lower bounds on the minimum pseudo-weight of linear codes
    Vontobel, PO
    Koetter, R
    2004 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2004, : 70 - 70
  • [4] A new algorithm for finding minimum-weight in large linear codes
    Canteaut, A
    CRYPTOGRAPHY AND CODING: 5TH IMA CONFERENCE, 1995, 1025 : 205 - 212
  • [5] Relaxation bounds on the minimum pseudo-weight of linear block codes
    Chaichanavong, P
    Siegel, PH
    2005 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), VOLS 1 AND 2, 2005, : 805 - 809
  • [6] Uncorrectable Errors of Weight Half the Minimum Distance for Binary Linear Codes
    Yasunaga, Kenji
    Fujiwara, Toru
    2008 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-6, 2008, : 975 - +
  • [7] Minimum distance computation of linear codes via genetic algorithms with permutation encoding
    Gomez-Torrecillas, Jose
    Lobillo, F. J.
    Navarro, Gabriel
    ACM COMMUNICATIONS IN COMPUTER ALGEBRA, 2018, 52 (03): : 71 - 74
  • [8] The minimum locality of linear codes
    Pan Tan
    Cuiling Fan
    Cunsheng Ding
    Chunming Tang
    Zhengchun Zhou
    Designs, Codes and Cryptography, 2023, 91 : 83 - 114
  • [9] The minimum locality of linear codes
    Tan, Pan
    Fan, Cuiling
    Ding, Cunsheng
    Tang, Chunming
    Zhou, Zhengchun
    DESIGNS CODES AND CRYPTOGRAPHY, 2023, 91 (01) : 83 - 114
  • [10] Minimum distance and the minimum weight codewords of Schubert codes
    Ghorpade, Sudhir R.
    Singh, Prasant
    FINITE FIELDS AND THEIR APPLICATIONS, 2018, 49 : 1 - 28
12345