the 3 isometry classes of irreducible [7,4,4]_9 codes are: code no 1: ================ 1 1 1 2 0 0 0 3 2 1 0 2 0 0 2 3 1 0 0 2 0 8 4 1 0 0 0 2 the automorphism group has order 2 and is strongly generated by the following 1 elements: ( 3 2 1 0 2 0 3 5 6 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 5)(3, 6)(4, 7) orbits: { 1, 5 }, { 2 }, { 3, 6 }, { 4, 7 } code no 2: ================ 1 1 1 2 0 0 0 3 2 1 0 2 0 0 6 3 1 0 0 2 0 7 4 1 0 0 0 2 the automorphism group has order 12 and is strongly generated by the following 3 elements: ( 6 0 0 0 0 7 0 5 0 , 1 , 0 0 4 2 0 0 0 1 0 , 0 , 4 1 2 6 3 5 8 8 8 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 3)(4, 5), (1, 2, 3)(4, 5, 6), (1, 4, 3, 6, 2, 5) orbits: { 1, 3, 5, 2, 4, 6 }, { 7 } code no 3: ================ 1 1 1 2 0 0 0 3 2 1 0 2 0 0 6 4 1 0 0 2 0 5 6 1 0 0 0 2 the automorphism group has order 42 and is strongly generated by the following 5 elements: ( 4 0 0 4 3 7 4 7 5 , 0 , 5 0 0 1 3 6 6 6 6 , 1 , 7 2 6 5 5 5 0 8 0 , 0 , 0 3 0 7 8 4 7 1 8 , 1 , 2 8 5 3 2 1 0 3 0 , 0 ) acting on the columns of the generator matrix as follows (in order): (2, 4, 6)(3, 7, 5), (2, 5)(3, 4)(6, 7), (1, 5, 6)(2, 3, 4), (1, 4, 6, 3, 5, 2), (1, 6, 4, 5, 2, 3, 7) orbits: { 1, 6, 2, 7, 4, 5, 3 }