Square (1,-1)-matrices with large determinants and near-Hadamard matrices
Square (1,-1)-matrices with large determinants and near-Hadamard matrices
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具有大行列式的方 (1,-1) 矩阵和近 Hadamard 矩阵
DOI：
10.1016/j.laa.2022.08.028
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发表时间：
2022
影响因子：
1.1
通讯作者：
Q. Xiang
中科院分区：
文献类型：
--
作者：
K. Momihara;S. Suda;Q. Xiang
给出了具有大数行列式的2模4同余阶(1，−1)-方阵的显式构造。特别地，我们基于两个块的几乎互补差集构造了九类准Hadamard矩阵，并计算了它们的行列式。作为推论，我们得到了许多几乎是D-最优的或至少具有80%D-有效性的(1，−，1)-矩阵。
We give explicit constructions of square (1,− 1)-matrices of order congruent to 2 modulo 4 with large determinants. In particular, we construct nine families of near-Hadamard matrices based on almost supplementary difference sets with two blocks, and compute their determinants. As consequences, we obtain many (1,− 1)-matrices which are almost D-optimal or have at least 80% D-efficiency.