The weight distribution and weight hierarchy of a linear code are two important research topics in coding theory. In this paper, by choosing proper defining sets from inhomogeneous quadratic functions over \({\mathbb {F}}_{q}^{2}\), we construct a family of three-weight p-ary linear codes and determine their weight distributions and weight hierarchies. Most of the codes can be used in secret sharing schemes.

中文翻译：

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p-ary 线性码族的权重分布和权重层次

线性编码的权重分布和权重层次是编码理论中的两个重要研究课题。在本文中，通过从\({\mathbb {F}}_{q}^{2}\) 上的非齐次二次函数中选择合适的定义集，我们构造了一个三权重p 元线性码族并确定它们的权重分布和权重层次结构。大多数代码可用于秘密共享方案。