2-(7,3,lambda;2) designs admitting the normalizer of a singer cycle as
an automorphism group
|
The Group A
Name:
Normalizer_singer_cycle7
Subgroup of GL(7,2)
Order: 889
Generator:
1 0 0 0 1 1 1
0 0 0 0 1 1 1
0 1 0 0 0 1 1
0 0 0 0 0 1 1
0 0 1 0 0 0 1
0 0 0 0 0 0 1
0 0 0 1 1 1 1
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: 3
Number of columns: 15
5 3 1 3 2 3 1 2 2 3 2
1 1 2 0
1 2 0 1 3 2 5 3 3 3 2 1 2 2 1
1 2 0 3 2 2 1 2 2 1 3 5 4 3 0
The orbits of A on the set
of 2-subspaces of GF(2)^7
Number of
orbits: 3
|
Nr |
Representative |
orbit
length |
|
0 |
[ 0 0 0 1 0 0 1 ] |
889 |
|
1 |
[ 0 0 1 0 0 0 0 ] |
889 |
|
2 |
[ 0 0 1 1 0 0 0 ] |
889 |
The orbits of A on the set
of 3-subspaces of GF(2)^7
Number of
orbits: 15
|
Nr |
Representative |
orbit
length |
|
0 |
[ 0 0 1 1 0 0 1 ] |
889 |
|
1 |
[ 0 0 0 1 0 1 1 ] |
889 |
|
2 |
[ 0 0 0 1 0 1 1 ] |
127 |
|
3 |
[ 0 0 1 0 1 1 1 ] |
889 |
|
4 |
[ 0 0 0 1 0 0 1 ] |
889 |
|
5 |
[ 0 1 1 1 1 0 1 ] |
889 |
|
6 |
[ 0 0 0 1 0 0 1 ] |
889 |
|
7 |
[ 0 0 0 1 1 1 1 ] |
889 |
|
8 |
[ 0 0 0 1 1 1 1 ] |
889 |
|
9 |
[ 0 0 1 0 1 1 1 ] |
889 |
|
10 |
[ 0 0 0 1 0 0 0 ] |
889 |
|
11 |
[ 0 1 0 0 1 0 1 ] |
889 |
|
12 |
[ 0 0 1 0 0 1 1 ] |
889 |
|
13 |
[ 0 1 0 0 1 0 1 ] |
889 |
|
14 |
[ 0 0 0 1 1 0 1 ] |
127 |
Solutions for lambda = 3
number of
solutions: 2
001000000000011
001000000010001
Solutions for lambda = 5
number of
solutions: 14
001000010000010
001010000000010
001000001000010
001000010010000
001010000010000
001000001010000
001000000100100
000001000000011
010000000000011
000001000010001
010000000010001
000100010000001
000110000000001
000100001000001
Solutions for lambda = 7
number of
solutions: 19
000001010000010
010000010000010
000011000000010
010010000000010
000001001000010
010000001000010
000001010010000
010000010010000
000011000010000
010010000010000
000001001010000
010000001010000
000100011000000
000110001000000
000110010000000
000000000110010
000001000100100
010000000100100
100000100001000
Solutions for lambda = 10
number of
solutions: 30
001001000100111
011000000100111
001001000110101
011000000110101
001100010100101
001110000100101
001100001100101
011001010000101
011011000000101
011001001000101
001001010101001
011000010101001
001011000101001
011010000101001
001001001101001
011000001101001
001001010010011
011000010010011
001011000010011
011010000010011
001001001010011
011000001010011
001100011000011
001110001000011
001110010000011
001100011010001
001110001010001
001110010010001
101000100001011
101000100011001
Solutions for lambda = 12
number of
solutions: 90
000101011000011
010100011000011
000111001000011
010110001000011
000111010000011
010110010000011
000101011010001
010100011010001
000111001010001
010110001010001
000111010010001
010110010010001
010001010010011
010011000010011
010001001010011
000100010110011
000110000110011
000100001110011
000101010100101
010100010100101
000111000100101
010110000100101
000101001100101
010100001100101
010001000100111
010001000110101
010001010101001
010011000101001
010001001101001
001001010100110
011000010100110
001011000100110
011010000100110
001001001100110
011000001100110
001001010110100
011000010110100
001011000110100
011010000110100
001001001110100
011000001110100
001100011100100
001110001100100
001110010100100
011001011000100
011011001000100
011011010000100
001001011101000
011000011101000
001011001101000
011010001101000
001011010101000
011010010101000
001001011010010
011000011010010
001011001010010
011010001010010
001011010010010
011010010010010
001110011000010
001110011010000
100000011000111
100010001000111
100010010000111
100000011010101
100010001010101
100010010010101
100010011001001
100001100001011
110000100001011
100001100011001
110000100011001
100100110001001
100110100001001
100100101001001
100100100000111
100100100010101
101000110001010
101010100001010
101000101001010
101000110011000
101010100011000
101000101011000
101000100010110
101000100101100
001101100101000
011100100101000
011101100000100
001101100010010
011100100010010
Solutions for lambda = 14
number of
solutions: 55
010001010100110
010011000100110
010001001100110
010001010110100
010011000110100
010001001110100
000101011100100
010100011100100
000111001100100
010110001100100
000111010100100
010110010100100
010001011101000
010011001101000
010011010101000
000111011000010
010110011000010
000111011010000
010110011010000
010001011010010
010011001010010
010011010010010
000100011110010
000110001110010
000110010110010
100010011000110
100010011010100
100001110001010
110000110001010
100011100001010
110010100001010
100001101001010
110000101001010
100001110011000
110000110011000
100011100011000
110010100011000
100001101011000
110000101011000
100100111001000
100110101001000
100110110001000
100000100111010
100100110000110
100110100000110
100100101000110
100100110010100
100110100010100
100100101010100
100001100010110
110000100010110
100001100101100
110000100101100
010101100010010
010101100101000
2001-10-05