Complete weight enumerators of a class of linear codes with two or three weights

被引：22
作者：
Kong, Xiangli [1 ]
Yang, Shudi [1 ]
机构：
[1] Qufu Normal Univ, Sch Math Sci, Jining 273165, Shandong, Peoples R China
来源：
DISCRETE MATHEMATICS | 2019年 / 342卷 / 11期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Linear code; Complete weight enumerator; Weight enumerator; Exponential sum; CYCLIC CODES; DISTRIBUTIONS; CONSTRUCTION;
D O I：
10.1016/j.disc.2019.06.025
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We construct a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. The results show that they have at most three weights and they are suitable for applications in secret sharing schemes. This is an extension of the results raised by Wang et al. (2017). (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：3166 / 3176
页数：11
相关论文
共 47 条
[1]   Complete weight enumerators of a class of linear codes [J].
Ahn, Jaehyun ;
Ka, Dongseok ;
Li, Chengju .
DESIGNS CODES AND CRYPTOGRAPHY, 2017, 83 (01) :83-99
[2]  
[Anonymous], 1977, THEORY ERROR CORRECT
[3]   On the complete weight enumerators of some reducible cyclic codes [J].
Bae, Sunghan ;
Li, Chengju ;
Yue, Qin .
DISCRETE MATHEMATICS, 2015, 338 (12) :2275-2287
[4]   WEIGHTS OF IRREDUCIBLE CYCLIC CODES [J].
BAUMERT, LD ;
MCELIECE, RJ .
INFORMATION AND CONTROL, 1972, 20 (02) :158-&
[5]   ON THE COMPLETE WEIGHT ENUMERATOR OF REED-SOLOMON CODES [J].
BLAKE, IF ;
KITH, K .
SIAM JOURNAL ON DISCRETE MATHEMATICS, 1991, 4 (02) :164-171
[6]   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
[7]  
Cary Huffman., 2003, Fundamentals of Error-Correcting Codes, DOI DOI 10.1017/CBO9780511807077
[8]   Cyclic codes with few weights and Niho exponents [J].
Charpin, P .
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2004, 108 (02) :247-259
[9]  
Coulter RS, 1998, ACTA ARITH, V83, P241
[10]  
Coulter RS, 2002, FINITE FIELDS TH APP, V8, P397, DOI [10.1006/ffta2001.0348, 10.1006/ffta.2001.0348]
12345