the 36 isometry classes of irreducible [10,5,3]_2 codes are:

code no       1:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 1 0 0 0 0 0 1 0
1 1 1 0 0 0 0 0 0 1
the automorphism group has order 144
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 0 1 
1 1 1 1 1 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
0 1 0 0 0 
0 1 1 0 0 
1 1 0 0 0 
0 0 0 0 1 
0 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(4, 6, 5), 
(2, 3)(5, 6)(7, 8), 
(2, 7)(3, 8)(5, 6), 
(1, 8, 9, 2)(3, 7)(4, 5)
orbits: { 1, 2, 3, 7, 9, 8 }, { 4, 5, 6 }, { 10 }

code no       2:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 1 0 0 0 0 0 1 0
1 0 0 1 0 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
1 0 1 0 0 
1 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(2, 8)(3, 7), 
(2, 7)(3, 8)
orbits: { 1 }, { 2, 8, 7, 3 }, { 4 }, { 5, 6 }, { 9 }, { 10 }

code no       3:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 1 0 0 0 0 0 1 0
1 1 1 1 0 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
0 1 0 0 0 
0 1 1 0 0 
1 1 0 0 0 
0 0 0 1 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(2, 7)(3, 8), 
(2, 3)(5, 6)(7, 8), 
(1, 8, 9, 2)(3, 7)(5, 6)
orbits: { 1, 2, 7, 3, 9, 8 }, { 4 }, { 5, 6 }, { 10 }

code no       4:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
1 1 1 0 0 0 0 0 1 0
0 1 0 1 0 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 1 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 1 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(1, 7)(4, 10)(8, 9)
orbits: { 1, 7 }, { 2 }, { 3 }, { 4, 10 }, { 5, 6 }, { 8, 9 }

code no       5:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
1 1 1 0 0 0 0 0 1 0
0 1 1 1 0 0 0 0 0 1
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 1 1 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 1 1 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(2, 3)(7, 8), 
(2, 7)(3, 8), 
(1, 9)(4, 10)(7, 8)
orbits: { 1, 9 }, { 2, 3, 7, 8 }, { 4, 10 }, { 5, 6 }

code no       6:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
1 1 1 0 0 0 0 0 1 0
1 1 1 1 0 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(2, 3)(5, 6)(7, 8), 
(2, 7)(3, 8)
orbits: { 1 }, { 2, 3, 7, 8 }, { 4 }, { 5, 6 }, { 9 }, { 10 }

code no       7:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
1 0 0 1 0 0 0 0 1 0
0 1 1 1 0 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 1 0 0 
1 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 0 1 0 
1 0 1 0 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 0 0 1 0 
0 1 0 0 0 
1 0 1 0 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(3, 8)(4, 9), 
(3, 9)(4, 8), 
(2, 7)(3, 8), 
(2, 3, 9)(4, 7, 8)(5, 6)
orbits: { 1 }, { 2, 7, 9, 4, 3, 8 }, { 5, 6 }, { 10 }

code no       8:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
1 0 0 1 0 0 0 0 1 0
1 1 1 1 0 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 1 0 0 
1 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 0 1 0 
1 0 1 0 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 0 0 1 0 
0 1 0 0 0 
1 0 1 0 0 
1 1 1 1 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(3, 8)(4, 9), 
(3, 9)(4, 8), 
(2, 3, 9)(4, 7, 8)(5, 6), 
(2, 7)(3, 8)
orbits: { 1 }, { 2, 9, 7, 4, 3, 8 }, { 5, 6 }, { 10 }

code no       9:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
1 0 0 1 0 0 0 0 1 0
1 0 0 0 1 0 0 0 0 1
the automorphism group has order 192
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 0 0 1 
1 0 0 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 1 0 0 
1 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 0 1 0 
1 0 1 0 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 0 0 1 
1 0 1 0 0 
0 0 0 1 0 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 0 0 0 1 
0 0 0 1 0 
1 0 1 0 0 
0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 9)(5, 10), 
(4, 10)(5, 9), 
(3, 8)(4, 9), 
(3, 9)(4, 8), 
(3, 9, 10)(4, 5, 8), 
(2, 3)(7, 8), 
(2, 5, 7, 10)(3, 9, 8, 4)
orbits: { 1 }, { 2, 3, 10, 8, 9, 4, 5, 7 }, { 6 }

code no      10:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
1 0 0 1 0 0 0 0 1 0
0 1 0 0 1 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 
0 1 0 0 0 
1 0 1 0 0 
1 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 0 1 0 
1 0 1 0 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 8)(4, 9), 
(3, 9)(4, 8)
orbits: { 1 }, { 2 }, { 3, 8, 9, 4 }, { 5 }, { 6 }, { 7 }, { 10 }

code no      11:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 0 1 0 0 0 0 1 0
0 0 1 1 0 0 0 0 0 1
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 0 1 0 
0 0 1 0 0 
0 0 0 0 1 
, 
0 0 0 1 0 
0 0 1 0 0 
0 1 0 0 0 
1 0 0 0 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(2, 3)(5, 6)(7, 8)(9, 10), 
(1, 2)(3, 4)(8, 9), 
(1, 4)(2, 3)(5, 6)(7, 10)(8, 9)
orbits: { 1, 2, 4, 3 }, { 5, 6 }, { 7, 8, 10, 9 }

code no      12:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 0 1 0 0 0 0 1 0
1 0 1 1 0 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
1 0 1 0 0 
1 1 0 0 0 
0 0 0 1 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(2, 8)(3, 7)(5, 6)(9, 10)
orbits: { 1 }, { 2, 8 }, { 3, 7 }, { 4 }, { 5, 6 }, { 9, 10 }

code no      13:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 0 1 0 0 0 0 1 0
1 1 1 1 0 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 0 1 0 
0 0 1 0 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(1, 2)(3, 4)(8, 9)
orbits: { 1, 2 }, { 3, 4 }, { 5, 6 }, { 7 }, { 8, 9 }, { 10 }

code no      14:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 0 1 0 0 0 0 1 0
1 1 0 0 1 0 0 0 0 1
the automorphism group has order 12
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 
0 1 0 0 0 
1 0 1 0 0 
0 1 0 1 0 
1 1 0 0 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 0 1 
0 0 0 1 0 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 0 1 0 
0 0 1 0 0 
0 0 0 0 1 
, 
1 1 0 0 0 
1 0 0 0 0 
1 1 0 0 1 
0 0 1 0 0 
0 1 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 8)(4, 9)(5, 10), 
(2, 7)(3, 8)(4, 5)(9, 10), 
(1, 2)(3, 4)(8, 9), 
(1, 2, 7)(3, 4, 10)(5, 8, 9)
orbits: { 1, 2, 7 }, { 3, 8, 4, 10, 9, 5 }, { 6 }

code no      15:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 0 1 0 0 0 0 1 0
0 0 1 0 1 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 0 1 
0 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 3)(4, 5)(7, 8)(9, 10)
orbits: { 1 }, { 2, 3 }, { 4, 5 }, { 6 }, { 7, 8 }, { 9, 10 }

code no      16:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 0 1 0 0 0 0 1 0
1 0 1 0 1 0 0 0 0 1
the automorphism group has order 10
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 
1 0 1 0 0 
1 1 0 0 0 
0 0 0 0 1 
0 0 0 1 0 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 0 1 0 
0 0 1 0 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(2, 8)(3, 7)(4, 5)(9, 10), 
(1, 2)(3, 4)(5, 6)(8, 9)
orbits: { 1, 2, 8, 9, 10 }, { 3, 7, 4, 5, 6 }

code no      17:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 0 1 0 0 0 0 1 0
0 1 1 0 1 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 1 0 0 0 
1 0 0 0 0 
0 0 0 1 0 
0 0 1 0 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(1, 2)(3, 4)(5, 6)(8, 9)
orbits: { 1, 2 }, { 3, 4 }, { 5, 6 }, { 7 }, { 8, 9 }, { 10 }

code no      18:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 1 1 0 0 0 0 1 0
1 1 1 1 0 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(2, 7)(3, 8)(5, 6), 
(2, 3)(5, 6)(7, 8)
orbits: { 1 }, { 2, 7, 3, 8 }, { 4 }, { 5, 6 }, { 9 }, { 10 }

code no      19:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 1 1 0 0 0 0 1 0
0 1 1 0 1 0 0 0 0 1
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 1 1 1 0 
0 1 1 0 1 
, 
1 0 0 0 0 
0 1 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 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 9)(5, 10), 
(4, 5)(9, 10), 
(2, 3)(7, 8), 
(2, 7)(3, 8)
orbits: { 1 }, { 2, 3, 7, 8 }, { 4, 9, 5, 10 }, { 6 }

code no      20:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
0 1 1 1 0 0 0 0 1 0
1 1 1 0 1 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
0 1 0 0 0 
1 0 1 0 0 
1 1 1 0 1 
0 1 1 1 0 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 8)(4, 10)(5, 9), 
(2, 3)(7, 8), 
(2, 7)(3, 8)
orbits: { 1 }, { 2, 3, 7, 8 }, { 4, 10 }, { 5, 9 }, { 6 }

code no      21:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 1 0 0
1 1 1 1 0 0 0 0 1 0
1 1 1 0 1 0 0 0 0 1
the automorphism group has order 32
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 1 1 0 1 
1 1 1 1 0 
, 
1 0 0 0 0 
0 1 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 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 1 1 1 1 
1 1 1 0 1 
1 1 1 1 0 
0 1 0 0 0 
0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 10)(5, 9), 
(4, 5)(9, 10), 
(2, 3)(7, 8), 
(2, 7)(3, 8), 
(1, 6)(2, 4, 7, 10)(3, 5, 8, 9)
orbits: { 1, 6 }, { 2, 3, 7, 10, 8, 9, 4, 5 }

code no      22:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 0
1 1 0 1 0 0 0 0 1 0
0 0 1 1 0 0 0 0 0 1
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
1 1 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 0 1 0 
1 1 1 0 0 
1 1 1 1 1 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(3, 8)(4, 9), 
(3, 9)(4, 8)(5, 6), 
(1, 2)
orbits: { 1, 2 }, { 3, 8, 9, 4 }, { 5, 6 }, { 7 }, { 10 }

code no      23:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 0
1 1 0 1 0 0 0 0 1 0
1 0 1 1 0 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
1 1 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 0 1 0 
1 1 1 0 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(3, 8)(4, 9), 
(3, 9)(4, 8)(5, 6)
orbits: { 1 }, { 2 }, { 3, 8, 9, 4 }, { 5, 6 }, { 7 }, { 10 }

code no      24:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 0
1 1 0 1 0 0 0 0 1 0
1 1 1 1 0 0 0 0 0 1
the automorphism group has order 32
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
1 1 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 0 1 0 
1 1 1 0 0 
1 1 1 1 1 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
0 0 0 0 1 
1 1 1 1 1 
1 1 0 1 0 
1 1 1 0 0 
0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(3, 8)(4, 9), 
(3, 9)(4, 8)(5, 6), 
(1, 2), 
(1, 6, 2, 5)(3, 8, 4, 9)(7, 10)
orbits: { 1, 2, 5, 6 }, { 3, 8, 9, 4 }, { 7, 10 }

code no      25:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 0
1 1 0 1 0 0 0 0 1 0
1 1 0 0 1 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 0 1 
0 0 0 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 1 0 1 0 
1 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
1 1 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 0 1 0 
1 1 1 0 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 0 0 1 
1 1 0 1 0 
0 0 1 0 0 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5)(9, 10), 
(4, 9)(5, 10), 
(3, 8)(4, 9), 
(3, 9)(4, 8), 
(3, 5, 8, 10)(4, 9), 
(1, 2)
orbits: { 1, 2 }, { 3, 8, 9, 10, 4, 5 }, { 6 }, { 7 }

code no      26:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 0
1 1 0 1 0 0 0 0 1 0
0 0 1 0 1 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 
0 1 0 0 0 
1 1 0 1 0 
1 1 1 0 0 
1 1 1 1 1 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 9)(4, 8)(5, 6), 
(1, 2)
orbits: { 1, 2 }, { 3, 9 }, { 4, 8 }, { 5, 6 }, { 7 }, { 10 }

code no      27:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 0
1 1 0 1 0 0 0 0 1 0
1 0 1 0 1 0 0 0 0 1
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
0 1 0 0 0 
1 1 0 1 0 
1 1 1 0 0 
1 1 1 1 1 
, 
0 1 0 0 0 
1 0 0 0 0 
1 1 1 0 0 
1 1 0 1 0 
0 0 0 0 1 
, 
1 1 1 0 0 
0 0 1 0 0 
0 1 0 0 0 
1 1 0 1 0 
1 0 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 9)(4, 8)(5, 6), 
(1, 2)(3, 8)(4, 9), 
(1, 8)(2, 3)(4, 9)(5, 10)
orbits: { 1, 2, 8, 3, 4, 9 }, { 5, 6, 10 }, { 7 }

code no      28:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 0
0 0 1 1 0 0 0 0 1 0
1 0 1 1 0 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
1 0 1 1 0 
0 0 1 0 0 
1 1 1 0 0 
0 0 0 0 1 
, 
0 0 1 0 0 
0 0 0 1 0 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(2, 10)(4, 8)(7, 9), 
(1, 3)(2, 4)(5, 6)(7, 9)(8, 10)
orbits: { 1, 3 }, { 2, 10, 4, 8 }, { 5, 6 }, { 7, 9 }

code no      29:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 0
0 0 1 1 0 0 0 0 1 0
1 1 1 1 0 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 1 1 1 1 
0 0 0 0 1 
0 0 0 1 0 
0 0 1 0 0 
1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(1, 2), 
(1, 5, 2, 6)(3, 4)(7, 10)
orbits: { 1, 2, 6, 5 }, { 3, 4 }, { 7, 10 }, { 8 }, { 9 }

code no      30:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 0
1 0 1 1 0 0 0 0 1 0
1 0 1 0 1 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 1 1 0 
1 0 1 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 1 0 1 
1 0 1 1 0 
, 
0 0 1 0 0 
1 1 1 0 0 
1 0 0 0 0 
1 0 1 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 9)(5, 10), 
(4, 10)(5, 9), 
(1, 3)(2, 8)(4, 9)
orbits: { 1, 3 }, { 2, 8 }, { 4, 9, 10, 5 }, { 6 }, { 7 }

code no      31:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 0 1 0 0
1 0 1 1 0 0 0 0 1 0
0 1 1 0 1 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
0 1 1 0 1 
1 0 1 1 0 
, 
0 0 1 0 0 
1 1 1 0 0 
1 0 0 0 0 
1 0 1 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 8)(4, 10)(5, 9), 
(1, 3)(2, 8)(4, 9)
orbits: { 1, 3, 8, 2 }, { 4, 10, 9, 5 }, { 6 }, { 7 }

code no      32:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
0 0 1 1 0 0 0 1 0 0
1 0 1 0 1 0 0 0 1 0
0 1 0 1 1 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 1 0 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 0 1 0 1 
, 
1 0 0 0 0 
1 1 0 0 0 
0 0 1 0 0 
0 0 1 1 0 
1 0 1 0 1 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 0 1 0 
0 0 1 0 0 
1 1 1 1 1 
, 
0 0 1 0 0 
0 0 0 1 0 
1 0 0 0 0 
0 1 0 0 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 10)(6, 9), 
(5, 9)(6, 10), 
(2, 7)(4, 8)(5, 9), 
(1, 2)(3, 4)(5, 6), 
(1, 3)(2, 4)(7, 8)
orbits: { 1, 2, 3, 7, 4, 8 }, { 5, 10, 9, 6 }

code no      33:
================
1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 0 1 1 0 0 0 1 0 0
1 0 1 0 1 0 0 0 1 0
1 0 0 1 1 0 0 0 0 1
the automorphism group has order 24
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 0 1 
0 0 0 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 1 0 1 
1 0 1 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 1 0 1 
1 0 0 1 1 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5)(8, 9), 
(4, 9)(5, 8), 
(3, 9)(4, 10)
orbits: { 1 }, { 2 }, { 3, 9, 8, 4, 5, 10 }, { 6 }, { 7 }

code no      34:
================
1 1 0 0 0 1 0 0 0 0
1 0 1 0 0 0 1 0 0 0
0 1 1 0 0 0 0 1 0 0
1 0 0 1 0 0 0 0 1 0
1 0 0 0 1 0 0 0 0 1
the automorphism group has order 32
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 0 0 1 
1 0 0 1 0 
, 
1 0 0 0 0 
1 0 1 0 0 
1 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 10), 
(4, 9), 
(4, 10)(5, 9), 
(2, 7)(3, 6), 
(2, 3)(6, 7)
orbits: { 1 }, { 2, 7, 3, 6 }, { 4, 9, 10, 5 }, { 8 }

code no      35:
================
1 1 0 0 0 1 0 0 0 0
1 0 1 0 0 0 1 0 0 0
0 1 1 0 0 0 0 1 0 0
1 1 1 1 0 0 0 0 1 0
1 1 1 0 1 0 0 0 0 1
the automorphism group has order 192
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 1 1 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 1 1 0 1 
0 0 0 1 0 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
0 1 1 0 0 
0 1 0 0 0 
1 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
0 1 0 0 0 
0 1 1 0 0 
1 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 10), 
(4, 9), 
(4, 5, 9, 10), 
(2, 6)(3, 7), 
(2, 3)(6, 7), 
(1, 8)(3, 6), 
(1, 7, 8, 2)(3, 6)
orbits: { 1, 8, 2, 7, 6, 3 }, { 4, 9, 10, 5 }

code no      36:
================
1 1 0 0 0 1 0 0 0 0
1 0 1 1 0 0 1 0 0 0
1 0 1 0 1 0 0 1 0 0
1 0 0 1 1 0 0 0 1 0
0 0 1 1 1 0 0 0 0 1
the automorphism group has order 336
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 0 0 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 1 1 0 
1 0 1 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 1 0 1 
1 0 1 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 0 0 1 
1 0 0 1 1 
1 0 1 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 1 1 
1 0 1 1 0 
1 0 0 1 1 
, 
1 0 0 0 0 
1 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 9)(8, 10), 
(5, 10)(8, 9), 
(4, 7)(5, 8), 
(4, 8)(5, 7), 
(3, 8, 5)(4, 7, 9), 
(3, 8, 9, 5, 7, 4, 10), 
(2, 6)
orbits: { 1 }, { 2, 6 }, { 3, 5, 10, 9, 8, 7, 4 }