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
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