the 4 isometry classes of irreducible [9,4,5]_4 codes are: code no 1: ================ 1 1 1 1 1 1 0 0 0 2 2 1 1 0 0 1 0 0 3 2 1 0 1 0 0 1 0 2 0 2 1 1 0 0 0 1 the automorphism group has order 4 and is strongly generated by the following 2 elements: ( 3 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 3 0 2 1 3 0 3 , 0 , 3 0 0 0 0 1 1 1 1 1 1 0 1 2 2 2 2 3 3 0 1 2 3 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(5, 8)(6, 9), (2, 6)(3, 9)(4, 7)(5, 8) orbits: { 1 }, { 2, 3, 6, 9 }, { 4, 7 }, { 5, 8 } code no 2: ================ 1 1 1 1 1 1 0 0 0 2 2 1 1 0 0 1 0 0 3 2 1 0 1 0 0 1 0 2 0 3 1 1 0 0 0 1 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 3 3 3 3 0 3 0 0 0 3 3 1 1 0 2 3 1 0 1 1 0 3 2 2 , 1 ) acting on the columns of the generator matrix as follows (in order): (1, 6)(3, 7)(4, 8)(5, 9) orbits: { 1, 6 }, { 2 }, { 3, 7 }, { 4, 8 }, { 5, 9 } code no 3: ================ 1 1 1 1 1 1 0 0 0 2 2 1 1 0 0 1 0 0 3 2 1 0 1 0 0 1 0 2 0 3 2 1 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 1 elements: ( 0 1 0 0 0 3 3 1 1 0 2 0 1 2 3 0 0 0 3 0 1 2 3 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (1, 8, 5, 9, 3, 6, 7, 2) orbits: { 1, 2, 7, 6, 3, 9, 5, 8 }, { 4 } code no 4: ================ 1 1 1 1 1 1 0 0 0 2 2 1 1 0 0 1 0 0 2 1 2 0 1 0 0 1 0 0 2 1 2 1 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 0 0 0 1 0 0 0 2 0 0 3 3 2 2 0 1 1 1 1 1 , 0 , 2 0 0 0 0 0 2 3 2 3 0 0 2 0 0 3 3 3 3 3 1 1 2 2 0 , 1 , 0 0 0 0 2 2 2 2 2 2 0 2 0 0 0 2 0 0 0 0 0 0 0 2 0 , 0 , 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 , 1 , 0 3 1 3 1 1 1 1 1 1 2 2 3 3 0 0 0 3 0 0 0 0 0 1 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 7, 4)(5, 9, 6), (2, 9)(4, 6)(5, 7), (1, 4, 5)(2, 3, 6), (1, 6)(2, 5)(3, 4), (1, 6, 2, 7, 3, 4, 5, 9) orbits: { 1, 5, 6, 9, 7, 4, 2, 3 }, { 8 }