the 3 isometry classes of irreducible [17,14,4]_16 codes are: code no 1: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 3 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 8 4 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 9 5 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 13 6 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 12 7 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 14 8 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 15 9 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 7 10 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 6 11 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 11 12 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 10 13 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 4 14 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 1 elements: ( 15 12 2 2 14 7 5 10 13 , 1 ) acting on the columns of the generator matrix as follows (in order): (1, 6, 15, 5, 17, 13, 14, 16)(2, 10, 8, 9, 3, 11, 12, 7) orbits: { 1, 16, 14, 13, 17, 5, 15, 6 }, { 2, 7, 12, 11, 3, 9, 8, 10 }, { 4 } code no 2: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 5 3 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 4 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 12 5 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 14 6 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 10 7 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 11 8 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 13 9 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 9 10 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 6 11 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 8 12 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 13 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 15 14 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 960 and is strongly generated by the following 6 elements: ( 5 0 0 0 15 0 0 0 8 , 2 , 5 0 0 0 8 0 13 12 7 , 3 , 13 0 0 3 15 1 5 1 9 , 1 , 4 0 0 7 15 10 4 11 7 , 2 , 4 9 1 3 1 14 8 5 1 , 3 , 12 2 14 2 13 4 1 2 12 , 0 ) acting on the columns of the generator matrix as follows (in order): (4, 6)(7, 14)(8, 11)(9, 12)(10, 13)(15, 17), (3, 16)(4, 7, 6, 14)(8, 13, 11, 10)(9, 15, 12, 17), (2, 12, 11, 6)(3, 8, 9, 10)(4, 13)(7, 15, 16, 14), (2, 6, 16, 10, 3, 15)(4, 14, 13, 12, 17, 8)(7, 11, 9), (1, 9, 11, 7)(2, 13, 12, 16)(3, 6)(4, 15, 10, 8), (1, 7, 3, 12, 17)(2, 16, 6, 14, 8)(4, 11, 15, 13, 9) orbits: { 1, 7, 17, 14, 4, 9, 11, 15, 12, 6, 16, 13, 8, 3, 2, 10 }, { 5 } code no 3: ================ 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 12 3 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 8 5 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 15 6 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 9 7 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 6 8 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 4 9 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 13 10 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 14 11 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 11 12 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 13 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 7 14 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 10 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 16320 and is strongly generated by the following 6 elements: ( 7 0 0 0 1 0 0 0 6 , 3 , 9 0 0 0 8 0 4 15 6 , 3 , 11 0 0 0 15 0 6 13 9 , 2 , 6 0 0 12 15 2 14 11 6 , 1 , 3 14 5 6 10 8 5 2 13 , 1 , 15 11 13 5 4 2 13 1 6 , 2 ) acting on the columns of the generator matrix as follows (in order): (4, 8, 7, 5)(6, 9)(10, 11, 17, 12)(13, 16, 14, 15), (3, 10, 12, 11)(4, 5, 13, 6)(7, 16)(8, 9, 15, 14), (3, 13, 6, 11, 9, 8)(4, 15, 10)(5, 17, 14, 16, 12, 7), (2, 6, 8, 12)(3, 14)(5, 9, 7, 15)(10, 13, 16, 11), (1, 12, 3, 8)(2, 4, 6, 14)(5, 13, 11, 7)(9, 10), (1, 13, 15, 11, 2, 7, 10, 5, 4, 17)(3, 12, 14, 9, 16)(6, 8) orbits: { 1, 8, 17, 4, 14, 9, 6, 3, 11, 5, 10, 2, 16, 15, 12, 13, 7 }