相互正交F—方的完备组

Heclayat与Seiden1970年提出了F—方及正交F—方的概念。有一种型的正交F—方完备组已由上述作者及其他人讨论过。本文目的在于讨论多种型的正交F—方完备组的存在性和构造方法。我们引进了正交均分组和直和子空间完备组的概念,并利用它们构造正交F—方的完备组,得到了某些情形下正交F—方完备组存在的充分必要条件。     

Nonisomorphic complete sets of orthogonal f-squares and hadamard matrices

Five nonisomorphic classes of Hadamard matrices of order 16 were given by Hall (1961). Three of these Hadamard classes have a 4 ×4 row and column structure; they generate three nonisomorphic complete sets of nine orthogonal F(4;2,2)-squares, one of which shows a previously unreported pattern. The remaining two Hadamard classes do not produce complete sets of F-squares, Each of the five Hadamard classes corresponds to a distinct set of single-degree-of-freedom contrasts in an analysis of variance.