A class of three-weight linear codes over finite fields of odd characteristic

被引：1

作者：

Duan, Bingbing ^{[1
]}

Han, Guangguo ^{[1
]}

Qi, Yanfeng ^{[1
]}

机构：

[1] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Peoples R China

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2024年 / 35卷 / 03期

关键词：

Linear code; Weight distribution; Additive character; Multiplicative character; Gauss sum; WEIGHT DISTRIBUTION; CONSTRUCTION; 2-WEIGHT;

D O I：

10.1007/s00200-022-00554-7

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Applied in communication, data storage system, secret sharing schemes, authentication codes and association schemes, linear codes attract much attention. In this paper, a class of three-weight linear codes is obtained by the defining sets over finite fields of odd characteristic. The parameters and weight distributions of linear codes are determined by the additive characters, multiplicative characters and Gauss sums. Further, most of linear codes obtained are minimal, which can be used to construct secret sharing schemes.

引用

页码：359 / 375

页数：17

共 34 条

[1] How to Build Robust Shared Control Systems [J].

Anderson R. ;

Ding C. ;

Helleseth T. ;

Kløve T. .

Designs, Codes and Cryptography, 1998, 15 (2) :111-124

[2]

CALDERBANK AR, 1984, PHILIPS J RES, V39, P143

[3] THE GEOMETRY OF 2-WEIGHT CODES [J].

CALDERBANK, R ;

KANTOR, WM .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1986, 18 :97-122

[4] 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

[5]

Cary Huffman., 2003, Fundamentals of Error-Correcting Codes

[6] SUBFIELD SUBCODES OF MODIFIED REED-SOLOMON CODES [J].

DELSARTE, P .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1975, 21 (05) :575-576

[7] Algebraic constructions of constant composition codes [J].

Ding, CS ;

Yin, JX .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (04) :1585-1589

[8] A coding theory construction of new systematic authentication codes [J].

Ding, CS ;

Wang, XS .

THEORETICAL COMPUTER SCIENCE, 2005, 330 (01) :81-99

[9] Cyclotomic linear codes of order 3 [J].

Ding, Cunsheng ;

Niederreiter, Harald .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2007, 53 (06) :2274-2277

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

Ding, Cunsheng .

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

← 1 2 3 4 →