the 4 isometry classes of irreducible [12,8,5]_16 codes are: code no 1: ================ 1 1 1 1 1 0 0 0 0 0 0 0 4 3 2 1 0 1 0 0 0 0 0 0 2 4 3 1 0 0 1 0 0 0 0 0 3 10 5 1 0 0 0 1 0 0 0 0 7 9 6 1 0 0 0 0 1 0 0 0 5 11 7 1 0 0 0 0 0 1 0 0 9 5 12 1 0 0 0 0 0 0 1 0 12 7 14 1 0 0 0 0 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 1 elements: ( 10 11 5 14 15 9 8 5 7 7 7 7 2 5 10 4 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 10, 7, 6)(2, 11, 9, 8)(3, 12, 4, 5) orbits: { 1, 6, 7, 10 }, { 2, 8, 9, 11 }, { 3, 5, 4, 12 } code no 2: ================ 1 1 1 1 1 0 0 0 0 0 0 0 4 3 2 1 0 1 0 0 0 0 0 0 3 8 5 1 0 0 1 0 0 0 0 0 11 15 6 1 0 0 0 1 0 0 0 0 15 9 7 1 0 0 0 0 1 0 0 0 12 6 8 1 0 0 0 0 0 1 0 0 10 4 9 1 0 0 0 0 0 0 1 0 7 13 10 1 0 0 0 0 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 1 elements: ( 3 5 15 8 0 8 0 0 4 4 4 4 8 13 5 9 , 3 ) acting on the columns of the generator matrix as follows (in order): (1, 12, 4, 7)(3, 11, 9, 5)(8, 10) orbits: { 1, 7, 4, 12 }, { 2 }, { 3, 5, 9, 11 }, { 6 }, { 8, 10 } code no 3: ================ 1 1 1 1 1 0 0 0 0 0 0 0 4 3 2 1 0 1 0 0 0 0 0 0 3 8 5 1 0 0 1 0 0 0 0 0 11 15 6 1 0 0 0 1 0 0 0 0 15 9 7 1 0 0 0 0 1 0 0 0 12 6 8 1 0 0 0 0 0 1 0 0 10 4 9 1 0 0 0 0 0 0 1 0 5 11 12 1 0 0 0 0 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 3 elements: ( 12 0 0 0 12 8 2 5 8 2 5 14 0 0 0 14 , 2 , 0 0 9 0 15 2 11 9 14 0 0 0 13 8 11 2 , 0 , 0 0 0 14 9 13 14 10 0 0 11 0 14 0 0 0 , 2 ) acting on the columns of the generator matrix as follows (in order): (2, 8)(3, 11)(5, 9)(6, 10)(7, 12), (1, 3)(2, 6)(4, 11)(5, 12)(7, 8)(9, 10), (1, 4)(2, 9)(5, 8)(6, 7)(10, 12) orbits: { 1, 3, 4, 11 }, { 2, 8, 6, 9, 7, 5, 10, 12 } code no 4: ================ 1 1 1 1 1 0 0 0 0 0 0 0 4 3 2 1 0 1 0 0 0 0 0 0 3 8 5 1 0 0 1 0 0 0 0 0 11 15 6 1 0 0 0 1 0 0 0 0 10 4 9 1 0 0 0 0 1 0 0 0 7 13 10 1 0 0 0 0 0 1 0 0 8 14 11 1 0 0 0 0 0 0 1 0 5 11 12 1 0 0 0 0 0 0 0 1 the automorphism group has order 240 and is strongly generated by the following 6 elements: ( 7 0 0 0 0 2 0 0 0 0 10 0 0 0 0 9 , 2 , 10 0 0 0 13 5 4 2 0 0 9 0 13 15 7 8 , 2 , 12 0 0 0 0 0 0 6 0 0 15 0 0 9 0 0 , 1 , 0 0 0 9 0 0 9 0 0 9 0 0 9 0 0 0 , 2 , 12 5 8 14 0 0 0 12 1 3 5 15 0 11 0 0 , 3 , 4 1 3 11 11 0 0 0 3 3 3 3 0 0 14 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 7)(6, 8)(9, 10)(11, 12), (2, 9)(4, 6)(7, 10)(8, 11), (2, 4)(5, 8, 7, 6)(9, 12, 10, 11), (1, 4)(2, 3)(6, 10)(8, 9), (1, 9, 10, 11)(2, 4)(3, 6, 8, 7), (1, 2, 8, 12)(3, 4, 10, 5)(6, 9) orbits: { 1, 4, 11, 12, 6, 2, 3, 8, 10, 9, 7, 5 }