From cxq01@nepthys.cs.uow.edu.au Thu Nov 25 14:02:01 1999 +1100 From: Cheng Xin Qu and Jooyeon Cho

Data from:
Hiroyuki Ohmori
On the classifications of weighing matrices of order 12.
The Journal of Combinatorial Mathematics and Combinatorial
Computing,Volume 5 April, 1989.

Classifications of weighing matrices of order 12 and weight 10
X_1
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - 1 - 1 1
1 - 0 - 1 1 - 0 - 1 1 1
- 1 - 0 1 - 1 - 0 1 1 1
- - 1 1 0 - - 1 1 0 1 1

X_2
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - - 1 1 1
1 - 0 - 1 1 - 0 1 - 1 1
- 1 - 0 1 - - 1 0 1 1 1
- - 1 1 0 - 1 - 1 0 1 1

X_2
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - - 1 1 1
1 - 0 - 1 1 - 0 1 - 1 1
- - 1 0 1 - 1 - 0 1 1 1
- 1 - 1 0 - - 1 1 0 1 1

There are three normal matrices of level 8, up to equivalence,
such that the first seven rows of each matrix equal those of X_1.
Moreover, for each matrix, it is possible to construct two normal
weighing matrices.

There are three normal matrices of level 5, up to equivalence,
such that the first four rows of each matrix equal those of X_2.

A1
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - 1 - 1 1
1 - 0 - 1 1 - 0 - 1 1 1
- 1 - 0 1 - 1 - 0 1 1 1
- - 1 1 0 - - 1 1 0 1 1
0 1 1 - - 0 - - 1 1 - 1
1 0 - 1 - - 0 1 - 1 - 1
1 - 0 - 1 - 1 0 1 - - 1
- 1 - 0 1 1 - 1 0 - - 1
- - 1 1 0 1 1 - - 0 - 1

A2
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - 1 - 1 1
1 - 0 - 1 1 - 0 - 1 1 1
- 1 - 0 1 - 1 - 0 1 1 1
- - 1 1 0 - - 1 1 0 1 1
0 1 1 - - 0 - - 1 1 - 1
1 0 - - 1 - 0 1 1 - - 1
1 - 0 1 - - 1 0 - 1 - 1
- - 1 0 1 1 1 - 0 - - 1
- 1 - 1 0 1 - 1 - 0 - 1

A3
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - 1 - 1 1
1 - 0 - 1 1 - 0 - 1 1 1
- 1 - 0 1 - 1 - 0 1 1 1
- - 1 1 0 - - 1 1 0 1 1
0 1 - 1 - 0 - 1 - 1 - 1
1 0 1 - - - 0 - 1 1 - 1
- 1 0 - 1 1 - 0 1 - - 1
1 - - 0 1 - 1 1 0 - - 1
- - 1 1 0 1 1 - - 0 - 1

A4
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - 1 - 1 1
1 - 0 - 1 1 - 0 - 1 1 1
- 1 - 0 1 - 1 - 0 1 1 1
- - 1 1 0 - - 1 1 0 1 1
0 1 - 1 - 0 - 1 - 1 - 1
1 0 - - 1 - 0 1 1 - - 1
- - 0 1 1 1 1 0 - - - 1
1 - 1 0 - - 1 - 0 1 - 1
- 1 1 - 0 1 - - 1 0 - 1

A5
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - 1 - 1 1
1 - 0 - 1 1 - 0 - 1 1 1
- 1 - 0 1 - 1 - 0 1 1 1
- - 1 1 0 - - 1 1 0 1 1
0 1 - - 1 0 - 1 1 - - 1
1 0 1 - - - 0 - 1 1 - 1
- 1 0 1 - 1 - 0 - 1 - 1
- - 1 0 1 1 1 - 0 - - 1
1 - - 1 0 - 1 1 - 0 - 1

A_6
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - 1 - 1 1
1 - 0 - 1 1 - 0 - 1 1 1
- 1 - 0 1 - 1 - 0 1 1 1
- - 1 1 0 - - 1 1 0 1 1
0 1 - - 1 0 - 1 1 - - 1
1 0 - 1 - - 0 1 - 1 - 1
- - 0 1 1 1 1 0 - - - 1
- 1 1 0 - 1 - - 0 1 - 1
1 - 1 - 0 - 1 - 1 0 - 1

A7
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - - 1 1 1
1 - 0 - 1 1 - 0 1 - 1 1
- 1 - 0 1 - - 1 0 1 1 1
- - 1 1 0 - 1 - 1 0 1 1
0 1 1 - - 0 - - 1 1 - 1
1 0 - 1 - - 0 1 1 - - 1
1 - 0 - 1 - 1 0 - 1 - 1
- 1 - 0 1 1 1 - 0 - - 1
- - 1 1 0 1 - 1 - 0 - 1

A8
1 1 1 1 1 1 1 1 1 1 0 0
1 1 1 1 1 - - - - - 0 0
0 1 1 - - 0 1 1 - - 1 1
1 0 - 1 - 1 0 - - 1 1 1
1 - 0 - 1 1 - 0 1 - 1 1
- - 1 0 1 - 1 - 0 1 1 1
- 1 - 1 0 - - 1 1 0 1 1
0 1 1 - - 0 - - 1 1 - 1
1 0 - - 1 - 0 1 - 1 - 1
1 - 0 1 - - 1 0 1 - - 1
- 1 - 0 1 1 1 - 0 - - 1
- - 1 1 0 1 - 1 - 0 - 1