the 36 isometry classes of irreducible [12,7,5]_5 codes are: code no 1: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 2 1 2 0 1 0 0 0 0 4 0 0 3 4 0 4 1 0 0 0 0 0 4 0 2 0 1 4 1 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 3 0 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(4, 5)(7, 10)(8, 9)(11, 12) orbits: { 1 }, { 2, 3 }, { 4, 5 }, { 6 }, { 7, 10 }, { 8, 9 }, { 11, 12 } code no 2: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 2 1 2 0 1 0 0 0 0 4 0 0 3 4 0 4 1 0 0 0 0 0 4 0 0 2 3 4 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 3: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 4 3 2 0 1 0 0 0 0 4 0 0 0 2 3 1 1 0 0 0 0 0 4 0 2 3 1 2 1 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 2 0 0 0 0 0 3 0 0 0 3 2 1 0 1 0 0 0 2 0 1 2 3 0 4 ) acting on the columns of the generator matrix as follows (in order): (3, 9)(5, 10)(6, 8)(7, 12) orbits: { 1 }, { 2 }, { 3, 9 }, { 4 }, { 5, 10 }, { 6, 8 }, { 7, 12 }, { 11 } code no 4: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 4 3 2 0 1 0 0 0 0 4 0 0 0 2 3 1 1 0 0 0 0 0 4 0 1 4 3 2 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 5: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 4 3 2 0 1 0 0 0 0 4 0 0 4 2 4 1 1 0 0 0 0 0 4 0 2 0 4 2 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 6: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 4 3 2 0 1 0 0 0 0 4 0 0 2 3 1 2 1 0 0 0 0 0 4 0 4 1 4 2 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 7: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 4 2 0 1 1 0 0 0 0 4 0 0 1 0 2 2 1 0 0 0 0 0 4 0 0 3 2 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 8: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 4 2 0 1 1 0 0 0 0 4 0 0 2 4 4 2 1 0 0 0 0 0 4 0 1 4 0 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 9: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 3 3 0 1 1 0 0 0 0 4 0 0 1 0 3 2 1 0 0 0 0 0 4 0 4 1 4 2 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 10: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 3 3 0 1 1 0 0 0 0 4 0 0 1 2 0 3 1 0 0 0 0 0 4 0 0 4 4 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 11: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 4 3 0 1 1 0 0 0 0 4 0 0 2 3 1 2 1 0 0 0 0 0 4 0 4 1 4 2 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 12: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 4 3 0 1 1 0 0 0 0 4 0 0 0 3 2 3 1 0 0 0 0 0 4 0 3 1 4 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 13: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 2 4 0 1 1 0 0 0 0 4 0 0 0 2 3 1 1 0 0 0 0 0 4 0 2 3 1 2 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 14: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 2 4 0 1 1 0 0 0 0 4 0 0 0 2 3 1 1 0 0 0 0 0 4 0 2 0 1 4 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 15: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 0 2 3 1 1 0 0 0 0 4 0 0 2 3 1 2 1 0 0 0 0 0 4 0 4 1 4 2 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 16: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 2 1 0 1 0 0 0 4 0 0 0 4 4 3 1 1 0 0 0 0 4 0 0 3 4 4 2 1 0 0 0 0 0 4 0 1 2 0 3 1 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 2 4 0 1 2 4 2 2 1 3 0 0 0 0 1 4 4 4 4 4 0 0 4 0 0 ) acting on the columns of the generator matrix as follows (in order): (1, 12)(2, 11)(3, 5)(4, 6) orbits: { 1, 12 }, { 2, 11 }, { 3, 5 }, { 4, 6 }, { 7 }, { 8 }, { 9 }, { 10 } code no 17: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 1 4 3 0 1 0 0 0 0 4 0 0 3 3 0 1 1 0 0 0 0 0 4 0 4 1 4 2 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 18: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 1 4 3 0 1 0 0 0 0 4 0 0 3 2 3 1 1 0 0 0 0 0 4 0 0 1 2 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 19: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 1 4 3 0 1 0 0 0 0 4 0 0 3 2 3 1 1 0 0 0 0 0 4 0 2 4 4 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 20: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 3 2 0 1 1 0 0 0 0 4 0 0 4 3 4 2 1 0 0 0 0 0 4 0 3 1 4 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 21: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 3 3 0 1 1 0 0 0 0 4 0 0 0 2 2 1 1 0 0 0 0 0 4 0 2 0 1 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 22: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 3 3 0 1 1 0 0 0 0 4 0 0 4 3 4 2 1 0 0 0 0 0 4 0 3 2 4 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 23: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 4 3 0 1 1 0 0 0 0 4 0 0 3 1 4 3 1 0 0 0 0 0 4 0 1 0 3 4 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 24: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 0 2 2 1 1 0 0 0 0 4 0 0 3 0 3 1 1 0 0 0 0 0 4 0 2 0 1 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 25: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 0 2 2 1 1 0 0 0 0 4 0 0 3 1 0 3 1 0 0 0 0 0 4 0 2 0 1 3 1 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 4 0 2 1 2 0 2 0 0 0 1 2 0 1 2 0 3 3 4 4 3 4 2 0 2 ) acting on the columns of the generator matrix as follows (in order): (1, 12)(3, 11)(4, 10)(5, 9)(6, 8) orbits: { 1, 12 }, { 2 }, { 3, 11 }, { 4, 10 }, { 5, 9 }, { 6, 8 }, { 7 } code no 26: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 0 2 2 1 1 0 0 0 0 4 0 0 2 0 1 3 1 0 0 0 0 0 4 0 4 1 0 4 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 27: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 3 0 3 1 1 0 0 0 0 4 0 0 4 3 4 2 1 0 0 0 0 0 4 0 3 1 4 3 1 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 3 4 4 0 0 4 0 0 0 3 1 2 1 0 0 0 0 1 0 1 2 1 3 4 ) acting on the columns of the generator matrix as follows (in order): (1, 7)(3, 8)(5, 11)(6, 10) orbits: { 1, 7 }, { 2 }, { 3, 8 }, { 4 }, { 5, 11 }, { 6, 10 }, { 9 }, { 12 } code no 28: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 3 0 3 1 1 0 0 0 0 4 0 0 4 3 4 2 1 0 0 0 0 0 4 0 3 4 4 3 1 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 1 elements: ( 4 3 1 3 0 0 2 0 0 0 2 0 0 0 0 0 0 0 4 0 4 0 4 3 3 ) acting on the columns of the generator matrix as follows (in order): (1, 3, 7, 8)(5, 6, 11, 10) orbits: { 1, 8, 7, 3 }, { 2 }, { 4 }, { 5, 10, 11, 6 }, { 9 }, { 12 } code no 29: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 3 0 3 1 1 0 0 0 0 4 0 0 4 3 4 2 1 0 0 0 0 0 4 0 1 3 0 4 1 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 1 elements: ( 4 3 1 3 0 0 2 0 0 0 2 0 0 0 0 0 0 0 4 0 4 0 4 3 3 ) acting on the columns of the generator matrix as follows (in order): (1, 3, 7, 8)(5, 6, 11, 10) orbits: { 1, 8, 7, 3 }, { 2 }, { 4 }, { 5, 10, 11, 6 }, { 9 }, { 12 } code no 30: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 3 0 3 1 1 0 0 0 0 4 0 0 2 0 1 3 1 0 0 0 0 0 4 0 3 2 4 3 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 31: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 0 2 4 1 1 0 0 0 0 4 0 0 4 1 0 2 1 0 0 0 0 0 4 0 3 4 4 3 1 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 1 elements: ( 0 4 0 0 0 1 1 3 3 0 0 0 4 0 0 3 0 0 0 0 3 2 0 4 2 ) acting on the columns of the generator matrix as follows (in order): (1, 4, 7, 2)(5, 9, 10, 11) orbits: { 1, 2, 7, 4 }, { 3 }, { 5, 11, 10, 9 }, { 6 }, { 8 }, { 12 } code no 32: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 4 2 1 0 1 0 0 0 4 0 0 0 1 0 2 2 1 0 0 0 0 4 0 0 2 0 1 3 1 0 0 0 0 0 4 0 4 1 0 4 1 0 0 0 0 0 0 4 the automorphism group has order 1 and is strongly generated by the following 0 elements: ( ) acting on the columns of the generator matrix as follows (in order): orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 } code no 33: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 2 3 1 0 1 0 0 0 4 0 0 0 3 4 2 0 1 0 0 0 0 4 0 0 0 2 2 1 1 0 0 0 0 0 4 0 3 0 3 1 1 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 4 0 0 0 1 0 0 0 0 0 0 3 0 0 3 3 3 3 3 1 3 4 0 2 ) acting on the columns of the generator matrix as follows (in order): (1, 2)(4, 6)(5, 10)(7, 11)(8, 12) orbits: { 1, 2 }, { 3 }, { 4, 6 }, { 5, 10 }, { 7, 11 }, { 8, 12 }, { 9 } code no 34: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 2 3 1 0 1 0 0 0 4 0 0 0 2 4 2 1 1 0 0 0 0 4 0 0 0 1 2 2 1 0 0 0 0 0 4 0 1 4 0 3 1 0 0 0 0 0 0 4 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 0 0 0 0 4 0 3 0 0 0 0 0 3 0 0 4 3 4 2 2 1 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(4, 10)(6, 11)(8, 12) orbits: { 1, 5 }, { 2 }, { 3 }, { 4, 10 }, { 6, 11 }, { 7 }, { 8, 12 }, { 9 } code no 35: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 2 3 1 0 1 0 0 0 4 0 0 0 2 4 2 1 1 0 0 0 0 4 0 0 3 4 3 2 1 0 0 0 0 0 4 0 1 0 4 4 1 0 0 0 0 0 0 4 the automorphism group has order 4 and is strongly generated by the following 1 elements: ( 2 0 0 0 0 1 2 4 2 0 3 1 3 4 4 1 0 4 4 1 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (2, 9, 6, 8)(3, 10)(4, 7, 11, 12) orbits: { 1 }, { 2, 8, 6, 9 }, { 3, 10 }, { 4, 12, 11, 7 }, { 5 } code no 36: ================ 1 1 1 1 1 4 0 0 0 0 0 0 2 2 1 1 0 0 4 0 0 0 0 0 3 1 2 1 0 0 0 4 0 0 0 0 3 3 1 0 1 0 0 0 4 0 0 0 1 4 4 0 1 0 0 0 0 4 0 0 2 3 4 2 1 0 0 0 0 0 4 0 0 3 2 3 1 0 0 0 0 0 0 4 the automorphism group has order 20 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 4 0 0 3 3 1 0 1 2 2 1 1 0 , 1 0 0 0 0 2 3 3 0 2 0 0 4 0 0 1 1 1 1 1 1 1 2 0 2 , 1 0 0 0 0 0 1 4 1 2 0 0 4 0 0 0 0 0 0 3 0 0 0 2 0 , 1 0 0 0 0 1 1 2 0 2 0 0 3 0 0 1 4 2 1 3 0 1 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (4, 9)(5, 7)(8, 10)(11, 12), (2, 10)(4, 6)(5, 9)(8, 11), (2, 12)(4, 5)(6, 7)(10, 11), (2, 5, 10, 9)(4, 8, 6, 11)(7, 12) orbits: { 1 }, { 2, 10, 12, 9, 8, 11, 5, 7, 4, 6 }, { 3 }