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

页码：433 / 452

页数：20

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