Complete Weight Enumerator for a Class of Linear Codes from Defining Sets and Their Applications

被引：0
作者：
Haibo Liu
Qunying Liao
Xiaofeng Wang
机构：
[1] Sichuan Normal University,Institute of Mathematics and Software Science
[2] Shenzhen University,College of Mathematics and Statistics
来源：
Journal of Systems Science and Complexity | 2019年 / 32卷
关键词：
Authentication codes; complete weight enumerator; constant composition codes; exponential sums; linear codes; secret sharing schemes; weight distributions;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an odd prime p, the complete weight enumerator of a class of p-ary linear codes based on defining sets are determined. Furthermore, from the explicit complete weight enumerator of linear codes, a new class of optimal constant composition codes and several classes of asymptotically optimal systematic authentication codes are obtained.
引用
收藏
页码：947 / 969
页数：22
相关论文
共 77 条
[1]  
Ding C S(2005)A coding theory construction of new systematic authentication codes Theor. Comput. Sci. 330 81-99
[2]  
Wang X(1998)How to build robust shared control systems Des. Codes Cryptogr. 15 111-124
[3]  
Anderson R(2005)Linear codes from perfect nonlinear mappings and their secret sharing schemes IEEE Trans. Inf. Theory 51 2089-2102
[4]  
Ding C S(1984)Three-weight codes and association schemes Philips J. Res. 39 143-152
[5]  
Helleseth T(2016)Complete weight enumerators of some linear codes and their applications Des. Codes Cryptogr. 81 153-168
[6]  
Carlet C(2015)A class of two-weight and three-weight codes and their applications in secret sharing IEEE Trans. Inf. Theory 61 5835-5842
[7]  
Ding C S(2006)On constant composition codes J. Combin. Mathe. Combin. Comput. 154 912-929
[8]  
Yuan J(2015)Linear codes from some 2-designs IEEE Trans. Inf. Theory 61 3265-3275
[9]  
Calderbank A R(2013)Hamming weights in irreducible cyclic codes Discret. Math. 313 434-446
[10]  
Goethals J M(2013)Five families of three-weight ternary cyclic codes and their duals IEEE Trans. Inf. Theory 59 7940-7946
12345678