摘要
文章考虑了极大弹性函数的构造问题。当(n,m)∈{(2r-1,r-1),(2r-1,r),(2r,r),(2r,r+1)}或者1≤m≤n/2+2-n/(2^(n/2+1)-2)时,构造了n元m维极大弹性函数,其非线性度为2n-1-2n-[m/2],代数次数为m-1。并对所构造的函数进行了计数。此外,满足构造条件的线性码的扩展码仍是满足构造条件的。最后讨论了两种其它满足构造条件的线性码的情况。
In this paper, we discuss the problem on construction of resilient functions with maximal resiliency. When the value of(n, m) is(2r-1,r-1),(2r-1,r),(2r,r),(2r,r+1),or 11≤m≤n/2+2-n/2n/2+1-2 we construct the n inputs m outputs functions with maximal resiliency. These constructed resilient functions possess the nonlinearity 2n-1-2n-[m/2] and the algebraic degree m -1 and we take count of these constructed resilient functions. Further, if linear [ n, m, t ] code satisfies the condition of the construction, then the linear [ n + 1, m, t + 1 ] code also satisfies the condition of the construction. We discuss other two kinds of linear codes which satisfy the condition of the construction in the end.
出处
《信息工程大学学报》
2007年第3期261-264,共4页
Journal of Information Engineering University
基金
国家自然科学基金资助项目(60673081)
关键词
弹性函数
线性码
非线性度
代数次数
resilient functions
linear codes
nonlinearity
algebraic degree