the 4 isometry classes of irreducible [10,5,4]_2 codes are: code no 1: ================ 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 the automorphism group has order 384 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 , 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 , 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 1 , 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (5, 6), (3, 4)(7, 8), (3, 7)(4, 8), (2, 8)(3, 9), (1, 9, 7)(2, 4, 10) orbits: { 1, 7, 8, 3, 9, 4, 2, 10 }, { 5, 6 } code no 2: ================ 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 , 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 , 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 , 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(7, 8), (3, 7)(4, 8), (2, 9)(4, 7)(5, 6), (1, 2, 9)(3, 7, 4)(5, 6, 10), (1, 5, 9, 10, 2, 6)(3, 4, 8) orbits: { 1, 9, 6, 2, 5, 10 }, { 3, 4, 7, 8 } code no 3: ================ 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 the automorphism group has order 720 and is strongly generated by the following 8 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 , 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 , 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 , 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 , 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 , 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 , 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 ) acting on the columns of the generator matrix as follows (in order): (4, 8)(5, 9)(6, 10), (3, 8)(4, 7)(5, 6), (3, 4)(7, 8)(9, 10), (2, 3)(4, 5)(8, 9), (2, 10, 3, 6)(4, 5, 9, 8), (1, 5)(2, 6)(7, 8), (1, 2, 9)(3, 7, 5)(4, 6, 8), (1, 10)(2, 8, 9, 3)(4, 7, 5, 6) orbits: { 1, 5, 9, 10, 6, 4, 7, 8, 2, 3 } code no 4: ================ 1 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 1 the automorphism group has order 1920 and is strongly generated by the following 9 elements: ( 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 , 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 , 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 , 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 , 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 , 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 , 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 , 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 , 0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (5, 9)(8, 10), (5, 8)(9, 10), (4, 7)(5, 8), (4, 8)(5, 7), (4, 5, 10)(7, 8, 9), (3, 6)(4, 7), (3, 4)(6, 7), (1, 6, 5)(2, 3, 8), (1, 9, 2, 10)(3, 4)(5, 8)(6, 7) orbits: { 1, 5, 10, 9, 8, 7, 4, 6, 2, 3 }