the 2 isometry classes of irreducible [10,7,3]_3 codes are: code no 1: ================ 1 1 1 2 0 0 0 0 0 0 1 1 0 0 2 0 0 0 0 0 2 1 0 0 0 2 0 0 0 0 1 0 1 0 0 0 2 0 0 0 2 0 1 0 0 0 0 2 0 0 0 1 1 0 0 0 0 0 2 0 2 1 1 0 0 0 0 0 0 2 the automorphism group has order 108 and is strongly generated by the following 7 elements: ( 2 0 0 0 1 0 0 0 1 , 2 0 0 0 1 0 1 0 1 , 1 0 0 0 1 0 2 0 1 , 2 0 0 0 2 0 1 1 1 , 2 0 0 1 0 2 2 2 0 , 2 0 0 0 0 2 0 2 0 , 2 0 0 2 1 1 2 2 0 ) acting on the columns of the generator matrix as follows (in order): (4, 10)(5, 6)(7, 8), (3, 7)(4, 9)(5, 6), (3, 7, 8)(4, 10, 9), (3, 4)(7, 9)(8, 10), (2, 8)(3, 5)(6, 7), (2, 3)(5, 7)(6, 8), (2, 8, 10)(3, 4, 5)(6, 7, 9) orbits: { 1 }, { 2, 8, 3, 10, 7, 6, 4, 5, 9 } code no 2: ================ 1 1 1 2 0 0 0 0 0 0 1 1 0 0 2 0 0 0 0 0 2 1 0 0 0 2 0 0 0 0 1 0 1 0 0 0 2 0 0 0 2 0 1 0 0 0 0 2 0 0 0 1 1 0 0 0 0 0 2 0 0 2 1 0 0 0 0 0 0 2 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 1 0 0 1 0 2 1 2 0 , 2 0 0 0 0 2 0 2 0 , 0 1 2 0 1 0 2 1 0 , 2 1 0 0 1 2 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (2, 8)(3, 6)(4, 9)(5, 7), (2, 3)(5, 7)(6, 8), (1, 10)(3, 6)(4, 7)(5, 9), (1, 8, 6)(2, 3, 10)(4, 5, 7) orbits: { 1, 10, 6, 3, 8, 2 }, { 4, 9, 7, 5 }