Construction of minimal binary linear codes with dimension n+3

被引：0
|
作者：
Shaikh, Wajid M. [1 ]
Jain, Rupali S. [1 ]
Reddy, B. Surendranath [1 ]
Patil, Bhagyashri S. [1 ]
机构：
[1] SRTMU Nanded, Sch Computat Sci, Nanded, India
来源：
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2025年 / 17卷 / 02期
关键词：
Linear code; Minimal code; Weight distribution; Ashikhmin-Barg condition;
D O I：
10.1007/s12095-024-00768-1
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, for n >= 6, we present the generic construction of binary linear codes of length 2(n) - 1 with dimension n + 3, and derive the necessary and sufficient condition for the constructed codes to be minimal. Using this generic construction, a new family of minimal binary linear codes violating the Ashikhmin-Barg condition will be constructed from a special class of Boolean functions. We also obtain the weight distribution of the constructed minimal binary linear codes. We will achieve minimal codes with the highest dimension, resulting in a better rate of transmission.
引用
收藏
页码：433 / 452
页数：20
相关论文
共 50 条
  • [31] Some new results on the minimum length of binary linear codes of dimension nine
    Dodunekov, S
    Guritman, S
    Simonis, J
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1999, 45 (07) : 2541 - 2544
  • [32] CONSTRUCTION OF MINIMAL LINEAR CODES FROM MULTI-VARIABLE FUNCTIONS
    Hyun, Jong Yoon
    Kim, Boran
    Na, Minwon
    ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2021, 15 (02) : 227 - 240
  • [33] On the VC-Dimension of Binary Codes
    Hu, Sihuang
    Weinberger, Nir
    Shayevitz, Ofer
    2017 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2017, : 594 - 598
  • [34] Wide minimal binary linear codes from the general Maiorana–McFarland class
    Fengrong Zhang
    Enes Pasalic
    René Rodríguez
    Yongzhuang Wei
    Designs, Codes and Cryptography, 2021, 89 : 1485 - 1507
  • [35] ON THE VC-DIMENSION OF BINARY CODES
    Hu, Sihuang
    Weinberger, Nir
    Shayevitz, Ofer
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2018, 32 (03) : 2161 - 2171
  • [36] The construction of periodically time-variant convolutional codes using binary linear block codes
    Ogasahara, Naonori
    Kobayashi, Manabu
    Hirasawa, Shigeichi
    ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE, 2007, 90 (09): : 31 - 40
  • [37] On the binary projective codes with dimension 6
    Bouyukliev, Iliya
    DISCRETE APPLIED MATHEMATICS, 2006, 154 (12) : 1693 - 1708
  • [38] An inductive construction of minimal codes
    Daniele Bartoli
    Matteo Bonini
    Burçin Güneş
    Cryptography and Communications, 2021, 13 : 439 - 449
  • [39] An inductive construction of minimal codes
    Bartoli, Daniele
    Bonini, Matteo
    Gunes, Burcin
    CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2021, 13 (03): : 439 - 449
  • [40] 关于方程(n+3)=(n)+2
    柯召
    孙琦
    四川大学学报(自然科学版), 1964, (01) : 1 - 8
12345