一类基于Kasami函数的极小线性码的构造

期刊菜单

一类基于Kasami函数的极小线性码的构造
Construction of a Class of Minimal Linear Codes Based on Kasami Functions

DOI: 10.12677/AAM.2023.128361, PDF, 下载: 139 浏览: 164
作者: 张莹中：西北师范大学，数学与统计学院，甘肃兰州
关键词: 布尔函数；Walsh变换；极小线性码；Boolean Function； Walsh Transform； Minimal Linear Codes

摘要: 布尔函数和线性码在设计序列密码共享方案等方面有重要的应用。本文基于Kasami函数构造了一类具有五值Walsh谱的布尔函数，研究了新函数的Walsh谱值分布，利用新函数构造了一类五重极小线性码。

Abstract: Boolean functions and linear codes with few-weights have important applications in designing sequence ciphers and in designing shared schemes. In this paper, we con- struct a class Boolean functions with five-valued Walsh spectra using Kasami functions and investigate the distribution of Walsh spectral values of the new functions. Final- ly, a class of minimal linear codes with five-weights is constructed by using the new functions.

文章引用：张莹中. 一类基于Kasami函数的极小线性码的构造[J]. 应用数学进展, 2023, 12(8): 3631-3638. https://doi.org/10.12677/AAM.2023.128361

参考文献

[1]	Rothaus, O. (1976) On Bent Functions. Journal of Combinatorial Theory, Series A, 20, 300- 305. https://doi.org/10.1016/0097-3165(76)90024-8
[2]	Ding, C., Helleseth, T., Klove, T. and Wang, X. (2007) A Generic Construction of Cartesian Authentication Codes. IEEE Transactions on Information Theory, 53, 2229-2235. https://doi.org/10.1109/TIT.2007.896872
[3]	Delsarte, P. (1973) Four Fundamental Parameters of a Code and Their Combinatorial Signifi- cance. Information and Control, 23, 407-438. https://doi.org/10.1016/S0019-9958(73)80007-5
[4]	Ding, C. and Wang, X. (2005) A Coding Theory Construction of New Systematic Authenti- cation Codes. Theoretical Computer Science, 330, 81-99. https://doi.org/10.1016/j.tcs.2004.09.011
[5]	Yuan, J. and Ding, C. (2006) Secret Sharing Schemes from Three Classes of Linear Codes. IEEE Transactions on Information Theory, 52, 206-212. https://doi.org/10.1109/TIT.2005.860412
[6]	Ashikhmin, A. and Barg, A. (1998) Minimal Vectors in Linear Codes. IEEE Transactions on Information Theory, 44, 2010-2017. https://doi.org/10.1109/18.705584
[7]	Ding, C. (2015) Linear Codes from Some 2-Designs. IEEE Transactions on Information Theory, 61, 3265-3275. https://doi.org/10.1109/TIT.2015.2420118
[8]	Ding, C. (2016) A Construction of Binary Linear Codes from Boolean Functions. Discrete Mathematics, 339, 2288-2303. https://doi.org/10.1016/j.disc.2016.03.029
[9]	Ding, C., Heng, Z. and Zhou, Z. (2018) Minimal Binary Linear Codes. IEEE Transactions on Information Theory, 64, 6536-6545. https://doi.org/10.1109/TIT.2018.2819196
[10]	Heng, Z., Ding, C. and Zhou, Z. (2018) Minimal Linear Codes over Finite Fields. Finite Fields and Their Applications, 54, 176-196. https://doi.org/10.1016/j.ffa.2018.08.010
[11]	Zhang, W., Yan, H. and Wei, H. (2019) Four Families of Minimal Binary Linear Codes with wmin/wmax ≤ 1/2. Applicable Algebra in Engineering, Communication and Computing, 30, 175-184. https://doi.org/10.1007/s00200-018-0367-x
[12]	Mesnager, S. (2014) Several New Infinite Families of Bent Functions and Their Duals. IEEE Transactions on Information Theory, 60, 4397-4407. https://doi.org/10.1109/TIT.2014.2320974
[13]	Ding, C., Heng, Z. and Zhou, Z. (2018) Minimal Binary Linear Codes. IEEE Transactions on Information Theory, 64, 6536-6545. https://doi.org/10.1109/TIT.2018.2819196

为你推荐

友情链接