论文标题
二进制II和II/III型互补阵列对的布尔功能
Boolean Functions of Binary Type-II and Type-II/III Complementary Array Pair
论文作者
论文摘要
长度为$ 2^{m} $的序列对从互补阵列对的互补阵列对$ \ Mathbf {2}}^{（M）} $和混合型II/III和大小$ \ Mathbf {2}^{（M-1）}^{（M-1）} \ TIME2 $ rcrpleentary sequence-sequece-sequece-sequie-sequece-yair and类型 - 和混合的类型-III/III和混合。详尽地搜索二进制II和III型互补序列对$ 2^{M} $（$ M = 1,2,3,4 $）表明它们都是从上述互补阵列对中预测的，其代数正常形式满足指定的表达式表达式。自然要问结论是否适用于所有$ m $。在本文中，我们证明了代数正常形式的这些表达式确定了所有二进制互补阵列对的所有二进制互补阵列对$ \ mathbf {2}^{（m）} $和混合型的type-ii/iii和大小$ \ mathbf {2}}^{（M-1）^{（M-1）}^{（M-1）}} \ tise 2 $。
The sequence pairs of length $2^{m}$ projected from complementary array pairs of Type-II of size $\mathbf{2}^{(m)}$ and mixed Type-II/III and of size $\mathbf{2}^{(m-1)}\times2$ are complementary sequence pairs Type-II and Type-III respectively. An exhaustive search for binary Type-II and Type-III complementary sequence pairs of small lengths $2^{m}$ ($m=1,2,3,4$) shows that they are all projected from the aforementioned complementary array pairs, whose algebraic normal forms satisfy specified expressions. It's natural to ask whether the conclusion holds for all $m$. In this paper, we proved that these expressions of algebraic normal forms determine all the binary complementary array pairs of Type-II of size $\mathbf{2}^{(m)}$ and mixed Type-II/III of size $\mathbf{2}^{(m-1)}\times2$ respectively.
