the 2 isometry classes of irreducible [10,2,7]_3 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 2 0 2 2 2 1 1 1 0 0 0 2 the automorphism group has order 1296 and is strongly generated by the following 8 elements: ( 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 1 , 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 , 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 , 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 , 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 2 2 2 2 2 2 2 2 , 2 2 2 2 2 2 2 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (8, 9), (7, 9), (5, 6)(7, 9), (4, 6, 5), (4, 7)(5, 9)(6, 8), (2, 3)(4, 5), (1, 2, 3)(4, 5)(7, 9, 8), (1, 5, 8, 3, 6, 7, 2, 4, 9) orbits: { 1, 3, 9, 2, 8, 7, 5, 4, 6 }, { 10 } code no 2: ================ 1 1 1 1 1 1 0 0 2 0 2 2 1 1 0 0 1 1 0 2 the automorphism group has order 576 and is strongly generated by the following 8 elements: ( 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 2 2 0 0 2 2 , 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 , 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 , 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 , 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 2 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 1 0 0 0 , 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 , 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 , 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 ) acting on the columns of the generator matrix as follows (in order): (8, 10), (7, 8), (6, 9), (5, 9, 6)(7, 8), (5, 8)(6, 10)(7, 9), (3, 4)(5, 6), (1, 2)(6, 9)(7, 8), (1, 4)(2, 3)(5, 6)(7, 8) orbits: { 1, 2, 4, 3 }, { 5, 6, 8, 9, 10, 7 }