有限域上最低异或数的MDS矩阵的构造

Construction of Minimum Xor number MDS Matrices in Limited Domain

研究了基于有限域GF(2)上利用循环矩阵、Hadamrd矩阵构造较低异或数的MDS矩阵。首先,构造异或数分别为0,1,2,3的一阶子矩阵A,然后利用子矩阵以循环矩阵、Hadamrd矩阵形式构造矩阵L或H,再利用判定定理判断是否为MDS矩阵,最终得到了异或总数为12的MDS矩阵。

In this paper, an MDS matrices based on limited domain （2） GF the circulant matricesand Hadamrd matrix is studied. First, exclusive xor number respectively 0,1,2,3 first-ordersubmatrix A is constructed, then the submatrix in the form of circulant matrices, Hadamrd matrixstructure matrix L is used to determine the judgment theorem for reusing MDS matrices, finally xortotal number of 12 MDS matrices is got.