On the Covering Structures of Two Classes of Linear Codes From Perfect Nonlinear Functions

Li C.; Ling S.; Qu L.

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On the Covering Structures of Two Classes of Linear Codes From Perfect Nonlinear Functions

机译：从完美非线性函数论两类线性码的覆盖结构

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摘要

In this paper, the weight distributions of two classes of linear codes based on all known explicit perfect nonlinear functions from $F_{q^{m}}$ to itself are determined using a unified approach. All the minimal codewords of these codes are characterized according to their weights, which suggests that their covering structures are determined. Finally, all the minimal access sets of the secret sharing schemes based on their dual codes are obtained.

机译：在本文中，使用统一的方法确定了基于所有已知的显式完美非线性函数的两类线性代码的权重分布，这些函数从$ F_ {q ^ {m}} $到其自身。这些代码的所有最小代码字均根据其权重进行特征化，这表明它们的覆盖结构已确定。最终，获得基于秘密共享方案的双码的所有最小访问集。

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《IEEE Transactions on Information Theory》 |2009年第1期|p.70-82|共13页
作者
Li C.; Ling S.; Qu L.;
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正文语种 eng
中图分类无线电电子学、电信技术;
关键词
Access structures; covering structures; perfect nonlinear functions; weight distributions;

机译：通道结构;覆盖结构;完善的非线性函数;权重分布;

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专利

1. Weight Distributions of Two Classes of Linear Codes from Perfect Nonlinear Functions [J] . DAI Qingping, LI Chao 电子学报：英文版 . 2009,第003期

机译：来自完美非线性函数的两类线性代码的权重分布
2. Linear Codes From Perfect Nonlinear Functions Over Finite Fields [J] . Wu Yanan, Li Nian, Zeng Xiangyong IEEE Transactions on Communications . 2020,第1期

机译：来自有限字段的完美非线性功能的线性码
3. The weight distribution of a class of linear codes from perfect nonlinear functions [J] . Jin Yuan, Carlet C., Cunsheng Ding IEEE Transactions on Information Theory . 2006,第2期

机译：来自完美非线性函数的一类线性码的权重分布
4. Construction of Perfect Nonlinear and Maximally Nonlinear Multi-output Boolean Functions Satisfying Higher Order Strict Avalanche Criteria [C] . Kishan Chand Gupta, Palash Sarkar 4th International Conference on Cryptology in India; Dec 8-10, 2003; New Delhi, India . 2003

机译：满足高阶严格雪崩准则的完美非线性和最大非线性多输出布尔函数的构造
5. Almost perfect nonlinear functions and related combinatorial structures. [D] . Maxwell, Mandi S. 2005

机译：几乎完美的非线性函数和相关的组合结构。
6. NONLINEAR TUBE-FITTING FOR THE ANALYSIS OF ANATOMICAL AND FUNCTIONAL STRUCTURES [O] . Jeff Goldsmith, Brian Caffo, Ciprian Crainiceanu, -1

机译：非线性TUBE-FOR拟合的解剖和功能结构的分析
7. Almost perfect nonlinear functions and related combinatorial structures [O] . Maxwell, Mandi S. 2005

机译：几乎完美的非线性函数和相关的组合结构
8. On p- and S-Functions and Related Classes of n-Dimensional Nonlinear Mappings [R] . More, J. J., Rheinboldt, W. C. 1970

机译：关于n维非线性映射的p-和s-函数及相关类

On the Covering Structures of Two Classes of Linear Codes From Perfect Nonlinear Functions

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