极大弹性函数的构造

Construction of Resilient Functions with Maximal Resiliency

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.