the 2 isometry classes of irreducible [7,3,5]_8 codes are: code no 1: ================ 1 1 1 1 1 0 0 4 3 2 1 0 1 0 2 5 3 1 0 0 1 the automorphism group has order 18 and is strongly generated by the following 3 elements: ( 6 0 0 0 0 0 0 4 0 0 5 0 1 7 2 3 , 2 , 5 5 5 5 0 1 0 0 0 0 7 0 0 0 0 3 , 2 , 3 1 4 7 1 1 1 1 0 0 4 0 2 7 1 6 , 0 ) acting on the columns of the generator matrix as follows (in order): (2, 7, 4), (1, 6, 5), (1, 7)(2, 5)(4, 6) orbits: { 1, 5, 7, 6, 2, 4 }, { 3 } code no 2: ================ 1 1 1 1 1 0 0 4 3 2 1 0 1 0 3 6 5 1 0 0 1 the automorphism group has order 42 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 0 6 3 1 2 4 2 2 2 2 , 2 , 7 0 0 0 2 3 1 4 0 1 0 0 5 2 6 4 , 1 , 5 5 5 5 0 0 0 1 0 7 0 0 0 0 3 0 , 1 , 0 2 0 0 4 1 3 2 3 3 3 3 7 0 0 0 , 1 , 3 6 5 1 6 4 3 7 0 4 0 0 6 6 6 6 , 0 ) acting on the columns of the generator matrix as follows (in order): (2, 5, 4)(3, 6, 7), (2, 3, 5, 6, 4, 7), (1, 6, 5)(2, 3, 4), (1, 4, 5, 3, 6, 2), (1, 5, 4, 6, 2, 3, 7) orbits: { 1, 5, 2, 7, 3, 6, 4 }