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本文证明了非仿射对称Boole函数的非零线性结构只能是全1向量,证明了具有非零恒变线性结构的奇数元对称平衡 Boole 函数(即 SBB 函数)恰是目前已构造出来的奇数元 SBB 函数,证明了偶数元 SBB 函数不具有恒变线性结构。本文还证明了目前所构造出的偶数元非仿射SBB函数均没有非零线性结构,并通过计算机验证了当n≤15时,2n元 SBB 函数和2n+元SSB 函数均没有非零不变线性结构。
This paper proves that the non-zero linear structure of the non-affine symmetric Boole function can only be an all-one vector. It is proved that the odd-bole symmetric balanced Boole function (that is, the SBB function) with a non-zero constant linear structure is just the odd Element SBB function, it is proved that the even-numbered SBB function does not have a constant linear structure. This paper also proves that none of the even-numbered non-affine SBB functions constructed at present have non-zero linear structure, and verified by computer that there is no non-zero invariance linearity for the 2n-ary SBB function and the 2n + structure.