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Linear Codes From Some 2-Designs

机译：某些2设计的线性代码

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摘要

A classical method of constructing a linear code over with a -design is to use the incidence matrix of the -design as a generator matrix over 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.
机译：用-design构建线性代码的经典方法是将-design的关联矩阵用作代码的生成矩阵。在文献中已经对该方法进行了广泛的研究。在本文中，研究了使用特定类别的2-设计构造线性代码的另一种方法，并且从几乎差集，差集和与半弯函数相关的2-设计类型中获得了具有少量权重的线性代码。本文获得的两个代码家族是最优的。本文介绍的线性代码除了在消费类电子产品，通信和数据存储系统中的应用外，还可以用于秘密共享和身份验证方案。提出了一种编码理论方法，用于表征高度非线性的布尔函数。

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