the 2 isometry classes of irreducible [10,5,6]_9 codes are: code no 1: ================ 1 1 1 1 1 2 0 0 0 0 5 4 3 2 1 0 2 0 0 0 4 7 6 3 1 0 0 2 0 0 6 8 4 5 1 0 0 0 2 0 7 2 8 6 1 0 0 0 0 2 the automorphism group has order 1440 and is strongly generated by the following 8 elements: ( 5 0 0 0 0 0 5 0 0 0 0 0 5 0 0 7 1 6 8 2 7 8 2 1 6 , 1 , 8 0 0 0 0 0 8 0 0 0 4 1 3 6 7 8 8 8 8 8 4 7 1 3 6 , 1 , 3 0 0 0 0 0 6 0 0 0 0 0 0 6 0 3 2 7 8 4 3 4 2 7 8 , 1 , 8 0 0 0 0 4 3 6 7 1 8 8 8 8 8 4 1 3 6 7 0 0 0 0 8 , 1 , 8 0 0 0 0 0 0 4 0 0 0 0 0 0 4 8 2 5 3 6 8 5 3 6 2 , 0 , 2 0 0 0 0 1 5 8 3 7 2 2 2 2 2 1 7 5 8 3 0 0 0 2 0 , 1 , 5 2 1 4 3 7 8 6 1 2 0 0 0 5 0 5 5 5 5 5 0 0 0 0 5 , 0 , 6 4 5 1 8 3 7 2 4 8 0 0 0 3 0 0 0 3 0 0 3 4 8 7 2 , 0 ) acting on the columns of the generator matrix as follows (in order): (4, 10)(5, 8)(6, 9), (3, 8)(4, 6)(5, 7), (3, 6, 7, 4)(5, 9, 8, 10), (2, 9)(3, 6)(4, 8), (2, 6, 7, 4, 9, 8, 5, 3), (2, 6, 3, 8, 7, 10)(4, 5, 9), (1, 6, 4, 3, 7, 2, 8, 9), (1, 10)(2, 7)(3, 4)(5, 9) orbits: { 1, 9, 10, 6, 5, 2, 4, 8, 7, 3 } code no 2: ================ 1 1 1 1 1 2 0 0 0 0 5 4 3 2 1 0 2 0 0 0 8 5 6 4 1 0 0 2 0 0 6 8 2 7 1 0 0 0 2 0 7 3 5 8 1 0 0 0 0 2 the automorphism group has order 720 and is strongly generated by the following 5 elements: ( 4 0 0 0 0 0 4 0 0 0 6 8 2 7 1 0 0 4 0 0 1 8 7 2 6 , 0 , 6 0 0 0 0 0 3 0 0 0 2 3 1 4 5 6 6 6 6 6 0 0 6 0 0 , 1 , 1 0 0 0 0 1 1 1 1 1 6 1 5 4 8 0 0 0 0 1 4 1 6 8 5 , 1 , 5 0 0 0 0 6 7 3 1 4 0 7 0 0 0 0 0 0 7 0 1 7 6 4 3 , 1 , 2 5 3 8 6 3 7 4 6 1 0 0 7 0 0 0 0 0 0 7 7 7 7 7 7 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 4, 7, 9)(5, 10, 6, 8), (3, 5, 9, 8, 7, 6, 4, 10), (2, 9, 7, 3, 8, 5, 4, 6), (2, 3, 8, 7, 9, 5, 6, 10), (1, 7, 8, 2, 6, 5, 4, 9) orbits: { 1, 9, 7, 5, 2, 4, 8, 3, 6, 10 }