2-(7,3,lambda;2) designs admitting a singer cycle as automorhism group |
The Group A
Name: Singer_cycle7
Subgroup of GL(7,2)
Order: 127
Generator:
0 0 0 0 0 0 1
1 0 0 0 0 0 0
0 1 0 0 0 0 0
0 0 1 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 1
The Kramer-Mesner Matrix M^A_{2,3}
Number of rows: 21
Number of columns: 93
3 1 1 1 1 1 1 1 1 1 1
1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0
1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0
1 1 1 1 0 0 1 0 1 1 0 0 0 0 3 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0
0 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 1 0 0 0 0 0 1
1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0
1 0 0 0 3 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0
0 0 1 0 1 0 1 1 0 0 0 0 0
1 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0
0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 3 0
0 0 0 0 0 1 0 0 1 1 1 0 0
1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0
1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1
3 0 0 0 0 1 0 0 1 1 1 0 0
0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0
1 1 1 1 0 0 0 3 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 1 0 0
0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 3 0 0
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0
0 0 0 0 0 1 1 1 1 1 0 0 1
0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 3
0 1 0 0 0 1 0 1 0 0 0 1 0
0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 3 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0
1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 1 1 0 1 1 0
0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 3 0 1 1 0 0 0
1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0
0 0 0 0 0 0 0 0 0 1 0 0 1
0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 3 0 1 0 1 0
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 1
0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1
0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 3 0 1 0 1 1 0 0 0 0 0 1 0 0 0
0 1 0 0 0 0 1 0 0 1 1 1 1
0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 1 3 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0
0 0 1 0 1 0 0 1 0 0 1 1 0
0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0
0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0
0 3 0 1 0 0 0 0 0 0 0 0 0
0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0
0 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 3 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 1 1 0 0 0 0 0 0
0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
0 1 3 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 1 1 0 0 1 1 0 1 0
0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 3 0 0
1 0 0 1 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 3 1 1 1 0 0 0 1 1 1 0 1 0 0 1 1
0 0 0 1 1 0 1 0 0 0 0 1 1
0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 3
1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0
1 0 1 1 1 0 1 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0
0 1 3 1 1 1 0 0 1 1 0 0 0
0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1
0 0 0 1 0 1 0 0 0 0 0 0 3 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0
0 0 0 0 0 0 0 1 0 0 1 0 1
The orbits of A on the set of 2-subspaces of GF(2)^7
Number of orbits: 21
|
Nr |
Representative |
orbit length |
|
0 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
1 |
[ 0 1 1 1 0 0 0 ] |
127 |
|
2 |
[ 0 0 1 0 1 1 1 ] |
127 |
|
3 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
4 |
[ 0 0 0 0 1 0 1 ] |
127 |
|
5 |
[ 0 0 1 1 0 0 0 ] |
127 |
|
6 |
[ 0 0 0 1 1 0 0 ] |
127 |
|
7 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
8 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
9 |
[ 0 0 0 0 1 1 1 ] |
127 |
|
10 |
[ 0 0 1 1 0 1 0 ] |
127 |
|
11 |
[ 0 0 1 0 0 1 0 ] |
127 |
|
12 |
[ 0 0 1 1 1 0 1 ] |
127 |
|
13 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
14 |
[ 0 0 1 0 0 1 1 ] |
127 |
|
15 |
[ 0 0 0 1 1 0 1 ] |
127 |
|
16 |
[ 0 1 0 1 0 0 1 ] |
127 |
|
17 |
[ 0 1 1 0 1 1 1 ] |
127 |
|
18 |
[ 0 1 1 0 1 1 1 ] |
127 |
|
19 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
20 |
[ 0 1 1 1 0 1 1 ] |
127 |
The orbits of A on the set of 3-subspaces of GF(2)^7
Number of orbits: 93
|
Nr |
Representative |
orbit length |
|
0 |
[ 0 0 0 1 0 1 1 ] |
127 |
|
1 |
[ 0 0 1 0 1 1 1 ] |
127 |
|
2 |
[ 0 0 0 0 0 1 1 ] |
127 |
|
3 |
[ 0 1 0 1 1 1 1 ] |
127 |
|
4 |
[ 0 0 1 1 0 0 1 ] |
127 |
|
5 |
[ 0 0 0 0 1 0 1 ] |
127 |
|
6 |
[ 0 0 0 0 0 1 1 ] |
127 |
|
7 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
8 |
[ 0 1 1 1 1 0 1 ] |
127 |
|
9 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
10 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
11 |
[ 0 0 0 1 0 1 1 ] |
127 |
|
12 |
[ 0 0 1 1 1 1 1 ] |
127 |
|
13 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
14 |
[ 0 0 1 1 0 1 1 ] |
127 |
|
15 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
16 |
[ 0 0 0 1 1 0 0 ] |
127 |
|
17 |
[ 0 0 0 1 0 0 0 ] |
127 |
|
18 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
19 |
[ 0 1 0 1 1 0 1 ] |
127 |
|
20 |
[ 0 0 0 1 0 0 0 ] |
127 |
|
21 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
22 |
[ 0 0 0 1 0 0 0 ] |
127 |
|
23 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
24 |
[ 0 0 0 0 1 0 0 ] |
127 |
|
25 |
[ 0 0 0 0 1 1 1 ] |
127 |
|
26 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
27 |
[ 0 1 0 1 1 1 1 ] |
127 |
|
28 |
[ 0 0 1 1 0 1 1 ] |
127 |
|
29 |
[ 0 0 0 1 1 1 0 ] |
127 |
|
30 |
[ 0 0 0 0 1 1 1 ] |
127 |
|
31 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
32 |
[ 0 0 0 0 0 1 1 ] |
127 |
|
33 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
34 |
[ 0 0 0 0 0 1 1 ] |
127 |
|
35 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
36 |
[ 0 0 0 0 1 1 1 ] |
127 |
|
37 |
[ 0 0 1 0 1 1 1 ] |
127 |
|
38 |
[ 0 0 0 0 1 0 1 ] |
127 |
|
39 |
[ 0 0 0 1 0 0 1 ] |
127 |
|
40 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
41 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
42 |
[ 0 0 0 1 0 1 0 ] |
127 |
|
43 |
[ 0 0 0 0 1 1 1 ] |
127 |
|
44 |
[ 0 0 1 1 1 0 1 ] |
127 |
|
45 |
[ 0 0 0 0 1 1 1 ] |
127 |
|
46 |
[ 0 0 0 0 1 1 1 ] |
127 |
|
47 |
[ 0 0 1 1 0 1 1 ] |
127 |
|
48 |
[ 0 0 0 1 0 1 1 ] |
127 |
|
49 |
[ 0 0 1 1 0 0 1 ] |
127 |
|
50 |
[ 0 0 0 1 0 1 0 ] |
127 |
|
51 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
52 |
[ 0 0 0 1 0 1 1 ] |
127 |
|
53 |
[ 0 0 0 1 1 0 1 ] |
127 |
|
54 |
[ 0 1 0 1 1 1 1 ] |
127 |
|
55 |
[ 0 1 0 0 1 1 1 ] |
127 |
|
56 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
57 |
[ 0 1 0 1 0 0 1 ] |
127 |
|
58 |
[ 0 0 1 1 0 1 1 ] |
127 |
|
59 |
[ 0 0 1 1 0 0 1 ] |
127 |
|
60 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
61 |
[ 0 0 1 1 0 1 1 ] |
127 |
|
62 |
[ 0 0 1 1 0 1 1 ] |
127 |
|
63 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
64 |
[ 0 1 0 1 0 0 1 ] |
127 |
|
65 |
[ 0 0 0 1 1 0 1 ] |
127 |
|
66 |
[ 0 0 0 0 1 0 1 ] |
127 |
|
67 |
[ 0 0 0 0 1 1 0 ] |
127 |
|
68 |
[ 0 0 0 0 1 1 0 ] |
127 |
|
69 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
70 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
71 |
[ 0 0 0 1 0 0 1 ] |
127 |
|
72 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
73 |
[ 0 0 0 0 1 0 1 ] |
127 |
|
74 |
[ 0 0 0 1 0 0 1 ] |
127 |
|
75 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
76 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
77 |
[ 0 0 1 1 1 1 1 ] |
127 |
|
78 |
[ 0 0 0 1 1 1 0 ] |
127 |
|
79 |
[ 0 0 1 1 1 1 1 ] |
127 |
|
80 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
81 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
82 |
[ 0 1 0 1 0 1 1 ] |
127 |
|
83 |
[ 0 0 0 0 0 1 1 ] |
127 |
|
84 |
[ 0 0 0 0 1 0 1 ] |
127 |
|
85 |
[ 0 0 1 1 1 1 1 ] |
127 |
|
86 |
[ 0 0 1 0 1 1 1 ] |
127 |
|
87 |
[ 0 0 0 0 1 0 1 ] |
127 |
|
88 |
[ 0 0 0 0 0 1 1 ] |
127 |
|
89 |
[ 0 0 0 1 1 1 1 ] |
127 |
|
90 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
91 |
[ 0 0 0 0 0 0 1 ] |
127 |
|
92 |
[ 0 0 0 0 0 1 0 ] |
127 |
Solutions for lambda = 3
number of
solutions: 100
Solutions for lambda = 4
number of
solutions: 3899
2001-10-05