Linear Codes From Some 2-Designs

被引：230
作者：
Ding, Cunsheng [1 ]
机构：
[1] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Hong Kong, Hong Kong, Peoples R China
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2015年 / 61卷 / 06期
关键词：
Almost bent functions; almost difference sets; bent functions; difference sets; linear codes; semibent functions; t-designs; HADAMARD DIFFERENCE SETS; BENT FUNCTIONS; CYCLIC CODES; WEIGHT DISTRIBUTIONS; NONLINEAR FUNCTIONS; CONSTRUCTIONS; SEQUENCES; FAMILY; SUMS;
D O I：
10.1109/TIT.2015.2420118
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
A classical method of constructing a linear code over GF(q) with a t-design is to use the incidence matrix of the t-design as a generator matrix over GF(q) of the code. This approach has been extensively investigated in the literature. In this paper, a different method of constructing linear codes using specific classes of 2-designs is studied, and linear codes with a few weights are obtained from almost difference sets, difference sets, and a type of 2-designs associated to semibent functions. Two families of the codes obtained in this paper are optimal. The linear codes presented in this paper have applications in secret sharing and authentication schemes, in addition to their applications in consumer electronics, communication and data storage systems. A coding-theory approach to the characterization of highly nonlinear Boolean functions is presented.
引用
收藏
页码：3265 / 3275
页数：11
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