论文标题
两类二进制线性代码的重量分布和重量层次结构
Weight distributions and weight hierarchies of two classes of binary linear codes
论文作者
论文摘要
具有几个权重的线性代码可以应用于通信，消费电子和数据存储系统。此外，线性代码的重量层次结构具有许多应用程序，例如在II型触角通道上，处理$ t $弹性功能以及线性代码的格子或分支复杂性等等。在本文中，我们首先提出一个公式，用于计算由定义集的广义方法构建的线性代码的重量层次结构。然后，我们构建了具有一些权重的两类二进制线性代码，并完全确定其重量分布和权重层次结构。它们的一些代码可以用于秘密共享方案中。
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with $t$-resilient functions and trellis or branch complexity of linear codes and so on. In this paper, we first present a formula for computing the weight hierarchies of linear codes constructed by the generalized method of defining sets. Then, we construct two classes of binary linear codes with a few weights and determine their weight distributions and weight hierarchies completely. Some codes of them can be used in secret sharing schemes.
