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

共 25 条

[1] Minimal vectors in linear codes [J].

Ashikhmin, A ;

Barg, A .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (05) :2010-2017

[2] Minimal Linear Codes in Odd Characteristic [J].

Bartoli, Daniele ;

Bonini, Matteo .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2019, 65 (07) :4152-4155

[3] Linear codes from perfect nonlinear mappings and their secret sharing schemes [J].

Carlet, C ;

Ding, CS ;

Yuan, J .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (06) :2089-2102

[4] Towards Secure Two-Party Computation from the Wire-Tap Channel [J].

Chabanne, Herve ;

Cohen, Gerard ;

Patey, Alain .

INFORMATION SECURITY AND CRYPTOLOGY - ICISC 2013, 2014, 8565 :34-46

[5] Linear codes from simplicial complexes [J].

Chang, Seunghwan ;

Hyun, Jong Yoon .

DESIGNS CODES AND CRYPTOGRAPHY, 2018, 86 (10) :2167-2181

[6]

Cohen Gerard D., 2013, Cryptography and Coding. 14th IMA International Conference, IMACC 2013. Proceedings: LNCS 8308, P85, DOI 10.1007/978-3-642-45239-0_6

[7] Minimal Binary Linear Codes [J].

Ding, Cunsheng ;

Heng, Ziling ;

Zhou, Zhengchun .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2018, 64 (10) :6536-6545

[8] A construction of binary linear codes from Boolean functions [J].

Ding, Cunsheng .

DISCRETE MATHEMATICS, 2016, 339 (09) :2288-2303

[9] A Class of Two-Weight and Three-Weight Codes and Their Applications in Secret Sharing [J].

Ding, Kelan ;

Ding, Cunsheng .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2015, 61 (11) :5835-5842

[10]

Du XN, 2023, DESIGN CODE CRYPTOGR, V91, P2273, DOI 10.1007/s10623-023-01198-5

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