Linear Codes From Some 2-Designs
Linear Codes From Some 2-Designs
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DOI：
10.1109/tit.2015.2420118
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发表时间：
2015-03
影响因子：
2.5
通讯作者：
C. Ding
中科院分区：
文献类型：
--
作者：
C. Ding
一种利用t -设计在有限域GF(q)上构造线性码的经典方法是将t -设计的关联矩阵用作该码在GF(q)上的生成矩阵。这种方法在文献中已被广泛研究。在本文中，研究了一种利用特定类别的2 -设计构造线性码的不同方法，并从几乎差集、差集以及一种与半 bent函数相关的2 -设计中得到了具有少量重量的线性码。本文得到的两类码是最优的。本文所呈现的线性码除了在消费电子、通信和数据存储系统中的应用外，在秘密共享和认证方案中也有应用。还提出了一种用编码理论方法来刻画高度非线性布尔函数的特征。
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.