the 2 isometry classes of irreducible [9,2,7]_5 codes are: code no 1: ================ 1 1 1 1 1 1 1 4 0 3 3 2 2 1 1 0 0 4 the automorphism group has order 64 and is strongly generated by the following 4 elements: ( 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 2 2 2 2 2 2 2 , 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 , 0 0 0 4 0 0 0 0 0 4 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 4 0 4 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 0 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (5, 6), (3, 4)(5, 6), (1, 6, 7, 4)(2, 5, 8, 3) orbits: { 1, 4, 3, 7, 8, 6, 5, 2 }, { 9 } code no 2: ================ 1 1 1 1 1 1 1 4 0 4 3 2 2 1 1 0 0 4 the automorphism group has order 48 and is strongly generated by the following 6 elements: ( 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 4 4 4 4 4 4 4 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 2 3 3 4 4 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 3 3 3 3 3 3 3 0 0 0 0 0 0 2 0 0 0 0 0 3 0 , 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 4 4 4 4 4 4 4 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 , 3 1 4 4 2 2 0 3 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 1 4 4 4 4 4 4 4 0 0 2 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (5, 6)(7, 8), (3, 4)(5, 6), (2, 9)(5, 8)(6, 7), (1, 2)(3, 8, 4, 7), (1, 2, 9)(3, 7, 5)(4, 8, 6) orbits: { 1, 2, 9 }, { 3, 4, 7, 5, 8, 6 }