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Weight distributions and weight hierarchies of a family of p-ary linear codes
Designs, Codes and Cryptography ( IF 1.4 ) Pub Date : 2021-10-29 , DOI: 10.1007/s10623-021-00962-9
Fei Li 1 , Xiumei Li 2
Affiliation  

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:

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。

更新日期:2021-10-30
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