the 2 isometry classes of irreducible [10,3,5]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 the automorphism group has order 128 and is strongly generated by the following 6 elements: ( 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 1 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 1 , 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 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 , 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 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 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 ) acting on the columns of the generator matrix as follows (in order): (7, 8), (5, 6), (3, 4)(5, 6), (3, 5)(4, 6)(7, 8)(9, 10), (1, 7, 2, 8)(3, 6)(4, 5), (1, 4)(2, 3)(5, 7)(6, 8) orbits: { 1, 8, 4, 7, 2, 6, 3, 5 }, { 9, 10 } code no 2: ================ 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 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 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 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 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 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 , 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (7, 10), (6, 9), (4, 8), (3, 5)(4, 9, 8, 6), (2, 5)(4, 10)(7, 8) orbits: { 1 }, { 2, 5, 3 }, { 4, 8, 6, 10, 9, 7 }