论文标题
关于Hadamard矩阵及其修改的Sylvester型结构
On Sylvester-type constructions of Hadamard matrices and their modifications
论文作者
论文摘要
利用在$ Q $ - ARPHABET上建立串联构造代码的想法，我们修改了Hadamard矩阵的已知广义Sylvester型结构。新建筑是基于两个Hadamard矩阵收藏的。尤其是这种结构涉及$ M $ HADAMARD的订单$ K $和$ K $ HADAMARD矩阵的订单$ M $。这些矩阵没有必要不同。结果，我们获得了订单$ km $的Hadamard矩阵。新建筑为新的Hadamard矩阵的建设提供了许多可能性，这些矩阵具有不同的等级和内核尺寸。
Using the ideas of concatenation construction of codes over the $q$-ary alphabet, we modify the known generalized Sylvester-type construction of the Hadamard matrices. The new construction is based on two collections of the Hadamard matrices. In particular this construction involves $m$ Hadamard matrices of order $k$ and $k$ Hadamard matrices of order $m$. These matrices are not necessary different. As a result we obtain a Hadamard matrix of order $km$. The new construction gives many possibilities for construction of the new Hadamard matrices with different ranks and dimension of kernel.
