the 2 isometry classes of irreducible [9,3,7]_8 codes are: code no 1: ================ 1 1 1 1 1 1 1 0 0 6 5 4 3 2 1 0 1 0 4 7 2 5 3 1 0 0 1 the automorphism group has order 168 and is strongly generated by the following 4 elements: ( 3 0 0 0 0 0 0 3 0 0 0 0 2 4 1 6 3 5 1 7 3 4 6 5 0 0 0 0 5 0 0 0 0 2 0 0 , 2 , 2 0 0 0 0 0 4 4 4 4 4 4 6 2 7 4 1 5 0 0 3 0 0 0 0 0 0 0 5 0 0 6 0 0 0 0 , 1 , 1 0 0 0 0 0 2 3 6 5 1 7 3 3 3 3 3 3 0 0 0 6 0 0 0 0 0 0 2 0 0 0 5 0 0 0 , 2 , 0 7 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 3 0 0 0 0 0 0 0 0 0 4 0 5 5 5 5 5 5 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 7, 8)(4, 6, 9), (2, 6, 7)(3, 4, 8), (2, 8, 9)(3, 6, 7), (1, 4, 2)(6, 8, 7) orbits: { 1, 2, 7, 9, 4, 3, 6, 8 }, { 5 } code no 2: ================ 1 1 1 1 1 1 1 0 0 6 5 4 3 2 1 0 1 0 3 2 5 4 7 1 0 0 1 the automorphism group has order 1512 and is strongly generated by the following 6 elements: ( 2 0 0 0 0 0 0 6 0 0 0 0 0 0 3 0 0 0 6 2 7 4 1 5 0 0 0 0 0 1 4 4 4 4 4 4 , 1 , 2 0 0 0 0 0 0 7 0 0 0 0 3 3 3 3 3 3 0 0 0 0 0 4 0 0 0 6 0 0 0 0 0 0 1 0 , 1 , 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 4 4 4 4 4 4 0 0 0 0 0 4 0 0 4 0 0 0 , 1 , 4 0 0 0 0 0 2 6 1 5 7 4 0 0 0 0 0 6 0 6 0 0 0 0 0 0 0 0 3 0 5 3 2 6 7 1 , 1 , 0 6 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 6 0 0 0 0 6 0 6 6 6 6 6 6 6 0 0 0 0 0 , 0 , 5 2 4 3 6 7 1 0 0 0 0 0 1 1 1 1 1 1 0 0 7 0 0 0 0 0 0 4 0 0 5 3 2 6 7 1 , 1 ) acting on the columns of the generator matrix as follows (in order): (4, 9, 8)(5, 7, 6), (3, 8, 7)(4, 5, 6), (2, 7, 4)(3, 6, 5), (2, 4, 9)(3, 8, 6), (1, 6, 3, 7, 5, 4, 2), (1, 2, 8, 6, 7, 3, 4, 5, 9) orbits: { 1, 2, 9, 4, 5, 8, 6, 7, 3 }