基于两类q元函数的极小线性码
Minimal linear codes from two classes of q-ary functions
何童童 1亓延峰1
作者信息
- 1. 杭州电子科技大学理学院,浙江 杭州 310018
- 折叠
摘要
线性码在通信和计算科学中有重要应用,也是密码理论与技术的重要工具.极小线性码作为一类特殊的线性码可应用于秘密共享、安全两方计算中,如何构造出新的具有好的性质的极小线性码是编码理论和应用的重要问题.本文考虑使用q元函数来构造线性码,选取特殊的q元函数构造了两类线性码,此类函数在一些固定重量的向量上满足某些性质.通过极小线性码的充要条件,证明了这两类线性码是极小线性码.
Abstract
Linear codes have important applications in communication and computer science,and are also important tools in cryptographic theory and technology.Minimal linear codes,a special class of linear codes,can be applied in secret sharing,secure two-party computation.How to construct new minimal linear codes with good parameters is an important problem in coding theory and cryptography.In this paper,we consider q-ary functions to construct linear codes.Two classes of linear codes are constructed by using special q-ary functions satisfying certain properties on vectors of fixed weight.By using necessary and sufficient conditions of minimal linear codes,we prove that two classes of linear codes are minimal linear codes.
关键词
线性码/极小线性码/q元函数/重量Key words
linear code/minimal linear code/q-ary function/weight引用本文复制引用
出版年
2024
NETL
NSTL
万方数据