On one class of symmetric Boolean functions

被引：0
作者：
机构：
[1] The Fourth Institute of Information Engineering University
[2] State Key Laboratory of Mathematical Engineering and Advanced Computing, Information Engineering University
来源：
Ou, Z.-H. | 2013年 / Editorial Board of Journal on Communications卷 / 34期
关键词：
Algebraic immunity; Correlation immunity; Nonlinearity; Symmetric Boolean functions;
D O I：
10.3969/j.issn.1000-436x.2013.01.010
中图分类号：
学科分类号：
摘要：
The properties of one class of symmetric Boolean functions which was denoted by ℜ was discussed, a different method for proving that one subclass of ℜ having maximum algebraic immunity was presented. A necessary condition was proposed for the functions of ℜ with maximum algebraic immunity, of which a lower bound of the number was also given. Meanwhile, the algebraic degree of most functions of ℜ was determined and linear structure and correlation immunity of ℜ were also analyzed. The results show that the functions of ℜ have no non-zero linear structure and only two functions of ℜ have 1-correlation immunity.
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页码：89 / 95+104
相关论文
共 14 条
  • [11] Wilson R.M., A diagonal form for the incidence matrices of t-subsets vs k-subsets, European Journal of Combinatorics, 11, 6, pp. 609-614, (1990)
  • [12] Canteaut A., Marion V., Symmetric Boolean functions, IEEE Trans Inf Theory, 51, 8, pp. 2791-2811, (2005)
  • [13] Chen Y.D., Lu P.Z., The nonlinearity of complementary symmetric Boolean functions, Computer Engineering & Science, 33, 10, pp. 51-56, (2011)
  • [14] Macwilliams F.J., Sloane N.J., The Theory of Error-Correcting Codes, (1977)
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