A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, ...A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, the known enumeration bounds of correlation-immune functions of order one are greatly improved. In fact, the best, up to now, lower bound is found.展开更多
n元m阶相关免疫对称函数的构造等价于方程sum C_（n-2）~iX_i from i=0 to （n-2）=sum C_（n-2）~iX_（i＋1） from i=0 to （n-2）在二元域上的求解。通过对该方程及其等价方程解的关系讨论,给出了构造奇数元二阶相关免疫对称函数的...n元m阶相关免疫对称函数的构造等价于方程sum C_（n-2）~iX_i from i=0 to （n-2）=sum C_（n-2）~iX_（i＋1） from i=0 to （n-2）在二元域上的求解。通过对该方程及其等价方程解的关系讨论,给出了构造奇数元二阶相关免疫对称函数的算法。展开更多
n元一阶相关免疫对称函数的构造等价于方程sum C_(n-1)~ix_i from i=0 to n-1=sum C_(n-1)~ix_(i+1) from i=0 to n-1在二元域上的求解。通过求解与其等价的方程C_(n-1)~0y_0+sum (C_(n-1)~i-C_(n-1)^(i-1))y_i=0 from i-1 to s构造了...n元一阶相关免疫对称函数的构造等价于方程sum C_(n-1)~ix_i from i=0 to n-1=sum C_(n-1)~ix_(i+1) from i=0 to n-1在二元域上的求解。通过求解与其等价的方程C_(n-1)~0y_0+sum (C_(n-1)~i-C_(n-1)^(i-1))y_i=0 from i-1 to s构造了一阶相关免疫对称函数,并在两种情形下给出了具体的构造和计数。展开更多
文摘A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, the known enumeration bounds of correlation-immune functions of order one are greatly improved. In fact, the best, up to now, lower bound is found.
文摘n元一阶相关免疫对称函数的构造等价于方程sum C_(n-1)~ix_i from i=0 to n-1=sum C_(n-1)~ix_(i+1) from i=0 to n-1在二元域上的求解。通过求解与其等价的方程C_(n-1)~0y_0+sum (C_(n-1)~i-C_(n-1)^(i-1))y_i=0 from i-1 to s构造了一阶相关免疫对称函数,并在两种情形下给出了具体的构造和计数。
