两类基于完全非线性函数的线性码

高莹,梅佳

系统科学与数学 ›› 2014, Vol. 34 ›› Issue (2) : 129-134.

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PDF(281 KB)
系统科学与数学 ›› 2014, Vol. 34 ›› Issue (2) : 129-134. DOI: 10.12341/jssms12255
论文

两类基于完全非线性函数的线性码

    高莹1,梅佳2
作者信息 +

TWO CLASSES OF LINEAR CODES BASED ON PERFECT NONLINEAR FUNCTIONS

    GAO Ying1, MEI Jia2
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文章历史 +

摘要

研究了Carlet等人所定义的两类基于完全非线性函数的线性码,给出了这两类线性码的生成矩阵.证明了对应的线性码是循环码时的两个充分条件.并指出两个完全非线性函数CCZ等价的充分必要条件是它们所对应的一类线性码置换等价.

Abstract

In this paper, the generator matrices of two classes of linear codes are given based on perfect nonlinear functions, which is defined by Carlet, etc, and two sufficient conditions are proven when the corresponding linear codes are cyclic. Finally, it is shown that two perfect nonlinear functions are CCZ equivalent to each ther if and only if the corresponding linear codes are permutation equivalent to each other.

关键词

完全非线性函数, 幂函数, 线性码,  / 循环码, 对偶码.

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高莹,梅佳. 两类基于完全非线性函数的线性码. 系统科学与数学, 2014, 34(2): 129-134. https://doi.org/10.12341/jssms12255
GAO Ying, MEI Jia. TWO CLASSES OF LINEAR CODES BASED ON PERFECT NONLINEAR FUNCTIONS. Journal of Systems Science and Mathematical Sciences, 2014, 34(2): 129-134 https://doi.org/10.12341/jssms12255
中图分类号: 94C10    94B05   
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