2-(6,3,lambda;q) designs admitting the direct product of a singer
cycle of dimension 5 with a fixed 1-subspace
|
The Group A
Name:
Singer_cycle5One1x
Subgroup of GL(6,2)
Order: 31
The Kramer-Mesner Matrix
M^A_{2,3}
Number of
rows: 21
Number of columns: 45
3 1 1 1 1 0 0 0 0 0 1
0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0
1 3 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0
0 0 1 0 0
1 1 3 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1
0 0 0 0 1
1 1 1 1 3 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0
0 1 0 0 0
1 1 1 3 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 0
0 0 0 0 0 2 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0
1 0 0 0 0
0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 2 0 0 0 0 0 0
0 0 0 0 1
0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 2 0
0 0 1 0 0
0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 2 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1
0 1 0 0 0
0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 2 1 0 0 0 0 0 1 1 0
0 0 0 1 0
0 0 0 0 0 0 1 2 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1
0 1 0 0 0
0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 2 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0
0 0 0 1 0
0 0 0 0 0 0 1 0 0 1 0 0 0 1 2 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1
0 0 1 0 0
0 0 0 0 0 0 1 0 0 0 2 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 1
0 0 0 1 0
0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 2 0 1 0 1 0 0 0 0 1 0 0
0 0 1 0 0
0 0 0 0 0 0 0 0 2 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0
0 0 0 0 1
0 0 0 0 0 0 0 0 0 1 1 0 1 2 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1
0 1 0 0 0
0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 2 1 0 0 1 0 1 1 0 0 1 1 0 0 0
0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 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 0 0 0 1 1 1 1 1 1 1 2 1 1 1 1 1
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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 3 3 3
The orbits of A on the set
of 2-subspaces of GF(2)^6
Number of
orbits: 21
Nr |
Representative |
orbit
length |
0 |
[ 0 0 0 1 0 0 ] |
31 |
1 |
[ 0 0 1 1 1 0 ] |
31 |
2 |
[ 0 0 0 1 1 0 ] |
31 |
3 |
[ 0 0 0 0 1 0 ] |
31 |
4 |
[ 0 0 1 1 1 0 ] |
31 |
5 |
[ 1 0 1 1 0 0 ] |
31 |
6 |
[ 1 0 1 1 1 0 ] |
31 |
7 |
[ 1 1 0 0 1 1 ] |
31 |
8 |
[ 1 0 1 1 0 0 ] |
31 |
9 |
[ 1 0 1 0 0 1 ] |
31 |
10 |
[ 1 0 1 0 1 1 ] |
31 |
11 |
[ 1 0 1 0 1 0 ] |
31 |
12 |
[ 1 0 1 0 0 0 ] |
31 |
13 |
[ 1 0 1 0 0 0 ] |
31 |
14 |
[ 1 0 1 1 0 0 ] |
31 |
15 |
[ 1 0 0 0 1 1 ] |
31 |
16 |
[ 1 0 1 0 1 1 ] |
31 |
17 |
[ 1 0 0 1 1 0 ] |
31 |
18 |
[ 1 0 0 1 1 0 ] |
31 |
19 |
[ 1 1 0 1 0 1 ] |
31 |
20 |
[ 1 0 0 0 0 0 ] |
31 |
The orbits of A on the set of 3-subspaces of GF(2)^6
Number of orbits: 45
Nr |
Representative |
orbit length |
0 |
[ 0 0 0 0 1 0 ] |
31 |
1 |
[ 0 0 0 1 1 0 ] |
31 |
2 |
[ 0 0 0 0 1 0 ] |
31 |
3 |
[ 0 0 0 0 1 0 ] |
31 |
4 |
[ 0 0 0 0 1 0 ] |
31 |
5 |
[ 1 1 0 0 0 1 ] |
31 |
6 |
[ 1 1 0 0 0 1 ] |
31 |
7 |
[ 1 1 0 0 1 1 ] |
31 |
8 |
[ 1 0 1 1 0 0 ] |
31 |
9 |
[ 1 1 0 0 0 1 ] |
31 |
10 |
[ 1 1 0 0 1 1 ] |
31 |
11 |
[ 1 1 0 0 0 1 ] |
31 |
12 |
[ 1 0 0 0 1 0 ] |
31 |
13 |
[ 1 0 0 0 1 0 ] |
31 |
14 |
[ 1 0 0 1 1 0 ] |
31 |
15 |
[ 1 0 1 1 0 0 ] |
31 |
16 |
[ 1 0 0 0 1 0 ] |
31 |
17 |
[ 1 0 1 1 1 0 ] |
31 |
18 |
[ 1 1 0 0 1 1 ] |
31 |
19 |
[ 1 1 1 0 1 1 ] |
31 |
20 |
[ 1 1 0 0 0 1 ] |
31 |
21 |
[ 1 1 0 1 1 1 ] |
31 |
22 |
[ 1 0 0 0 1 0 ] |
31 |
23 |
[ 1 0 1 1 0 0 ] |
31 |
24 |
[ 1 0 0 0 1 0 ] |
31 |
25 |
[ 1 0 0 0 1 0 ] |
31 |
26 |
[ 1 0 0 0 1 0 ] |
31 |
27 |
[ 1 0 0 1 1 0 ] |
31 |
28 |
[ 1 0 0 1 0 0 ] |
31 |
29 |
[ 1 0 1 1 0 0 ] |
31 |
30 |
[ 1 0 0 0 1 1 ] |
31 |
31 |
[ 1 0 1 0 1 0 ] |
31 |
32 |
[ 1 0 1 1 0 0 ] |
31 |
33 |
[ 1 1 0 1 0 1 ] |
31 |
34 |
[ 1 1 0 1 0 1 ] |
31 |
35 |
[ 1 0 0 1 0 1 ] |
31 |
36 |
[ 1 1 0 1 1 1 ] |
31 |
37 |
[ 1 0 0 1 1 0 ] |
31 |
38 |
[ 1 1 0 1 0 1 ] |
31 |
39 |
[ 1 1 0 0 0 1 ] |
31 |
40 |
[ 1 0 0 0 0 0 ] |
31 |
41 |
[ 1 0 0 0 0 0 ] |
31 |
42 |
[ 1 0 0 0 0 0 ] |
31 |
43 |
[ 1 0 0 0 0 0 ] |
31 |
44 |
[ 1 0 0 0 0 0 ] |
31 |
Solutions for lambda = 6
number of solutions: 330
001100100001011010110000001010001101011001010
001100000001111010110000001110010100011001010
001100000001011110110010000110001101001001010
001100000000011111100100001110011100001001010
001010000001111110110010000110000101001010010
001010000000111111100100001110010100001010010
001010100000011111100100001010001101001010010
001010100001111010110000001010000101011010010
101000100001011110110010000010001101001011000
101000100000011111100100001010011100001011000
101000000001111110110010000110010100001011000
101000100001111010110000001010010100011011000
100010100001111010110010000010000101011010001
100010100000111011100100001010010100011010001
100010000000111111100110000110010100001010001
100010100000011111100110000010001101001010001
100100100001011010110010000010001101011001001
100100100000011011100100001010011100011001001
100100000001111010110010000110010100011001001
100100000000011111100110000110011100001001001
000110000001111010110010000110000101011000011
000110000000111011100100001110010100011000011
000110100000011011100100001010001101011000011
000110000000011111100110000110001101001000011
001100000001011011110000101010110101000011000
000110000001011011101110000010110101000010001
011000101000111010101001000001001101001010010
001100001000111010100001100101001101001000110
101000101000111010100001100001001101001010100
110000101000111010101001000000011100001110001
100100001000111010100001100100011100001100101
010100001000111010101001000100011100001100011
001100000010111010010101010111000100001010010
100100100010011010010101010010001100001110001
100100001001011001101001010010010110100001010
100010001101011001100001110010000111000010010
110000101101110000010001010100001100001110010
110000101100110001000101010101001100001010010
100100101001110000010001010100001100101100110
100100101000110001000101010101001100101000110
100101000001010010110010010011100100100101100
100011000101010010100110010011100100000110100
110001000101010010110010010011100100000111000
010101000000010011110000011011100100100101010
010011000100010011100100011011100100000110010
000111000000010011100100011011100100100100110
011000010110001101100001001000101110100001010
001010010111101000100001001000100110110000110
101000010111001100100011000000101110100001100
100010010111101000100011000000100110110000101
110000010110001101100011000000101110100001001
010010010110101001100001001000100110110000011
010100101011001000011001010000001111010001010
010100001011101000011001010100010110010001010
010100001010001101010001110100001111000001010
010100001010001101001101010100011110000001010
010010001010101101010001110100000111000010010
010010001010101101001101010100010110000010010
010010101010001101001101010000001111000010010
010010101011101000011001010000000111010010010
000110001011101000001101010100010110010000110
000110001011101000010001110100000111010000110
000110101011001000001101010000001111010000110
000110001010001101000101110100001111000000110
100100101011001000001101010000011110010001100
100100101011001000010001110000001111010001100
100100001011101000010001110100010110010001100
100100001010001101000101110100011110000001100
100010001010101101000101110100010110000010100
100010101010001101000101110000001111000010100
100010101011101000001101010000010110010010100
100010101011101000010001110000000111010010100
110000101010001101010001110000001111000011000
110000101010001101001101010000011110000011000
110000001010101101010001110100010110000011000
110000101011101000011001010000010110010011000
110000010010101101010101010001000110010010010
100100010011001100010101010000001110010100110
010011000010001110110000011010000110010101010
100011000010001110100110010011000110010001100
010100000110001011100101000101110100010001001
010100000111001010110001000100110100010101001
010100100010001011110001000001100101110001001
010100000010001111110001000100110100100101001
010010100111001010110001000000100101010110001
010010100110001011100101000001100101010010001
010010000110001111100101000100110100000110001
010010100010001111110001000000100101100110001
000110100011001010110001000000100101110100101
000110100010001011100101000001100101110000101
000110000111001010100101000100110100010100101
000110000010001111100101000100110100100100101
001100100011001010110001000001100101110001100
001100000111001010100101000101110100010001100
001100000010001111100101000101110100100001100
001100000011001110110001000100110100100101100
001010100011001110110001000000100101100110100
001010100010001111100101000001100101100010100
001010000111001110100101000100110100000110100
001010100111001010100101000001100101010010100
011000000110001111100101000101110100000011000
011000000111001110110001000100110100000111000
011000100010001111110001000001100101100011000
011000100111001010110001000001100101010011000
010100001010001110100011000101010101010001100
010010101010001110100001001000010101010110100
010011000010100110010110010101100100000110100
010011100010100010010100011001100100010110100
010101100010000010010100011001101100010101100
010101000010000110010110010101101100000101100
010011101010100000001010011000101110100001100
010011001110100000000010111100101110000001100
011000010111010100010011010110000011000010010
011000010110010101000101011110010010000010010
011000110010010101010001011010000011100010010
011000110111010000010001011010000011010010010
001100010011010100010011010110000011100000110
001100010010010101000101011110010010100000110
001100110011010000010001011010000011110000110
001100010111010000000101011110010010010000110
101000110011010100010011010010000011100010100
101000110010010101000101011010010010100010100
101000010111010100000111010110010010000010100
101000110111010000000101011010010010010010100
110000110010010101010011010010000011100010001
110000010110010101000111010110010010000010001
110000110111010000010011010010000011010010001
110000110110010001000101011010010010010010001
100100110011010000010011010010000011110000101
100100110010010001000101011010010010110000101
100100010111010000000111010110010010010000101
100100010010010101000111010110010010100000101
010100010111010000010011010110000011010000011
010100010110010001000101011110010010010000011
010100110010010001010001011010000011110000011
010100010010010101010011010110000011100000011
011001100110010000010101010110001011000000011
101001100010110000010101010110010010100000101
101000110101010001100001100000101011100000101
101000010101110001100001100100110010100000101
011000110101010001101001000000101011100000011
011000010101110001101001000100110010100000011
110001100000010011110000110011000011010001001
110001100000010011101100010011010010010001001
110001100001010010111000010010010010010101001
110001000000010111110000110110010010000101001
100011100001010010101100010010010010010100101
100011100001010010110000110010000011010100101
100011100000010011100100110011000011010000101
100011000000010111100100110110010010000100101
010011100001010010111000010010000011010100011
010011100000010011101100010011000011010000011
010011000000010111110000110110000011000100011
010011000000010111101100010110010010000100011
011001000000010111110000110111000011000001010
011001000000010111101100010111010010000001010
011001000001010110111000010110010010000101010
011001100001010010111000010011000011010001010
001011000001010110101100010110010010000100110
001011000001010110110000110110000011000100110
001011000000010111100100110111000011000000110
001011100001010010101100010011000011010000110
101001000000010111100100110111010010000001100
101001000001010110110000110110010010000101100
101001100001010010101100010011010010010001100
101001100001010010110000110011000011010001100
100010100101010011100000110110000010011001001
001010100001010111101000010110000010101001010
001010010010110110000010111110000010001010100
001100010010010110000010111110001010001001100
011000110010010110001010011010001010001011000
010010110010110010001010011010000010011010001
010100110010010010001010011010001010011001001
000110010010110010000010111110000010011000101
011001010000110010101000101000111010000100101
011001010000110010101010100001101011000000101
001100010010011010100001101010010011010000101
011000010010011110101011000010010011000010001
011001010100000101010100101001101001000110010
011001010101000100011110000001101001000110010
011001010000100101011100001001110000100110010
011001010101100000011100001001110000010110010
001101010001100000011100001001110000110100110
001101010101000000010100101001101001010100110
001101010000000101010100101001101001100100110
001101010001000100011110000001101001100100110
101001010101000100010110100001101001000110100
101001010000100101010100101001110000100110100
101001010001100100011110000001110000100110100
101001010101100000010100101001110000010110100
110001010100100001010100101001110000010110001
110001010101100000011110000001110000010110001
110001010100000101010110100001101001000110001
110001010000100101011110000001110000100110001
100101010101000000010110100001101001010100101
100101010000100001010100101001110000110100101
100101010001100000011110000001110000110100101
100101010000000101010110100001101001100100101
010101010000100001011100001001110000110100011
010101010100000001010100101001101001010100011
010101010101000000011110000001101001010100011
010101010000000101011110000001101001100100011
001011101000100001001100101001110001100010100
001011101001100000011000101000110001100110100
001011001101100000001110100101110001000010100
001011101101000000001100101000111001000110100
001101101000000001001100101001111001100001100
001101101001000000011000101000111001100101100
001101001101000000001110100101111001000001100
001101001001100000011010100101110001100001100
011001001101100000011010100101110001000011000
011001101000100001011000101001110001100011000
011001101100000001001100101001111001000011000
011001101101000000011000101000111001000111000
010101001101000000011010100100111001000101001
010101001100000001001110100101111001000001001
010101101000000001011000101000111001100101001
010101001000100001011010100101110001100001001
010011001101100000011010100100110001000110001
010011001100100001001110100101110001000010001
010011101000100001011000101000110001100110001
010011101100000001001100101000111001000110001
000111101000000001001100101000111001100100101
000111001101000000001110100100111001000100101
000111001001100000011010100100110001100100101
000111001000100001001110100101110001100000101
011001101000100100011010000101001001101001010
011001101000100100011000001100011000101101010
011001101100100000010000101101001001011001010
011001101100100000001100001101011000011001010
001011101000100100010000101100001001101100110
001011101000100100001100001100011000101100110
001011101000100100001110000101001001101000110
001011101100100000000100101101001001011000110
101001101000100100001110000101011000101001100
101001101000100100010010100101001001101001100
101001101000100100010000101100011000101101100
101001101100100000000100101101011000011001100
110001101100100000001110000101011000011001001
110001101100100000010010100101001001011001001
110001101100100000010000101100011000011101001
110001101000100100011010000100011000101101001
100011101100100000000100101100011000011100101
100011101100100000000110100101001001011000101
100011101000100100001110000100011000101100101
100011101000100100010010100100001001101100101
010011101100100000010000101100001001011100011
010011101100100000001100001100011000011100011
010011101100100000001110000101001001011000011
010011101000100100011010000100001001101100011
101001110000100100010100001001001000111100110
110001010100100100010110000101001000011100011
100010111001100100001010001000010000111110100
100010111000100101000010101001000001111010100
100010011101100100000010101100010000011110100
100010111101000100000010101000001001011110100
100100111001000100001010001000011000111101100
100100111000000101000010101001001001111001100
100100011101000100000010101100011000011101100
100100011000100101000010101101010000111001100
110000011100100101000010101101010000011011000
110000111000100101001010001001010000111011000
110000111101000100001010001000011000011111000
110000111100000101000010101001001001011011000
010010011101100100001010001100010000011110010
010010011100100101000010101101000001011010010
010010111000100101001010001001000001111010010
010010111101000100001010001000001001011110010
010100011101000100001010001100011000011101010
010100011100000101000010101101001001011001010
010100111000000101001010001001001001111001010
010100011000100101001010001101010000111001010
000110011101000100000010101100001001011100110
000110111001000100001010001000001001111100110
000110011001100100001010001100010000111100110
000110011000100101000010101101000001111000110
010100011101000001001010101001110001010011000
000110011001000101001010101000110001100110100
001100110101000001001100001001101000111001010
001100010101100001010000101101100000111001010
001100010101000101010000101100101000101101010
001100010101000101001110000101101000101001010
001010010101100101010000101100100000101110010
001010010101100101001110000101100000101010010
001010110101000101001100001000101000101110010
001010110101100001001100001001100000111010010
101000110101000101010000101000101000101111000
101000110101000101001110000001101000101011000
101000010101100101010010100101100000101011000
101000110101100001010000101001100000111011000
100100110101000001010000101000101000111101001
100100110101000001001110000001101000111001001
100100010101100001010010100101100000111001001
100100010101000101010010100100101000101101001
100010110101100001010000101000100000111110001
100010110101100001001110000001100000111010001
100010010101100101010010100100100000101110001
100010110101000101001110000000101000101110001
000110010101100001010000101100100000111100011
000110010101100001001110000101100000111000011
000110110101000001001100001000101000111100011
000110010101000101001110000100101000101100011
001010101101100001001000101100110000101011000
000110101101000001001010100100101001101001001
101001100100100001010100100101101000101001001
001011100101100000011100000100101000101100011
110001011000100100010010101001010001010110100
010101011000000100001110001001011001010100110
100011001101001000101010100010010011010001001
100011001000001101101010100010010011100001001
001011001000001101101000101010010011100001010
001011001101001000101000101010010011010001010
100101001010001000011001110010010010100101001
100011001110001000001101110010010010000110001
000111001010001000011001110010000011100100011
001101001010001000011001110011000011100001010
001011001110001000001101110011000011000010010
101001001110001000001101110011010010000011000
001100010010001110010010101011000001011011000
001100010010001110001110001011010000011011000
000110010010001110010010101010000001011110001
000110010010001110001110001010010000011110001
001100010110001010001101100001101000001110001
001100010010101010011001100001100000101110001
100100011101010000001011010011000000101110010
100100011100010001000001111011000000101110010
100011001100101000100010001011000100111001010
100011001100001100100010001010001100101101010
010010100010110011100001010100100110100000101
011000100111010010100001010100101110000001100
2001-10-05