the 2 isometry classes of irreducible [9,5,5]_9 codes are: code no 1: ================ 1 1 1 1 2 0 0 0 0 4 3 2 1 0 2 0 0 0 8 2 3 1 0 0 2 0 0 5 8 4 1 0 0 0 2 0 7 5 6 1 0 0 0 0 2 the automorphism group has order 72 and is strongly generated by the following 2 elements: ( 1 0 0 0 4 4 4 4 0 3 0 0 7 5 8 2 , 1 , 8 8 8 8 6 8 2 1 4 7 3 5 3 1 2 4 , 1 ) acting on the columns of the generator matrix as follows (in order): (2, 3, 6, 8, 7, 9, 4, 5), (1, 6, 2, 7, 3, 8, 4, 5) orbits: { 1, 5, 4, 9, 8, 7, 6, 3, 2 } code no 2: ================ 1 1 1 1 2 0 0 0 0 4 3 2 1 0 2 0 0 0 7 6 3 1 0 0 2 0 0 8 4 5 1 0 0 0 2 0 2 8 6 1 0 0 0 0 2 the automorphism group has order 144 and is strongly generated by the following 5 elements: ( 5 0 0 0 0 5 0 0 1 6 8 2 8 2 1 6 , 1 , 3 0 0 0 5 4 8 1 3 3 3 3 1 5 4 8 , 1 , 2 0 0 0 0 0 2 0 8 5 7 3 5 7 3 8 , 0 , 0 0 3 0 3 0 0 0 4 8 1 5 5 4 8 1 , 1 , 1 6 8 2 0 5 0 0 6 8 2 1 5 5 5 5 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 9)(4, 7)(5, 8), (2, 7)(3, 5)(4, 6), (2, 8, 4, 5, 6, 9, 7, 3), (1, 2, 8, 3)(4, 5, 6, 7), (1, 9)(3, 6)(4, 5) orbits: { 1, 3, 9, 5, 7, 8, 6, 4, 2 }