the 4 isometry classes of irreducible [18,2,9]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 14631321600 and is strongly generated by the following 19 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 1 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (16, 17), (15, 16), (15, 16, 17), (14, 15, 16), (13, 16, 14), (12, 16), (11, 15, 12), (11, 14, 13)(16, 17), (10, 12, 15, 13, 14, 16)(11, 17), (9, 15, 13, 14, 16, 10, 12)(11, 17), (7, 8)(9, 10, 12, 13, 17, 14, 15, 16, 11), (6, 8)(9, 14, 13, 11)(10, 16, 17, 12, 15), (5, 7)(9, 15, 10)(11, 12, 16, 13, 14, 17), (5, 8)(6, 7)(9, 12, 11, 13, 10, 17, 15, 16), (4, 7, 5, 8)(9, 17, 10, 15, 13, 14, 11), (3, 8, 7)(9, 15, 12, 17, 16, 11, 14, 10), (2, 8, 6, 3)(5, 7)(9, 13, 17)(10, 16, 15)(11, 14, 12), (2, 3, 4, 8, 6, 5, 7)(9, 12)(11, 14, 15, 17)(13, 16), (1, 8, 6, 3, 4, 2, 5, 7)(9, 17, 11, 15, 10, 16, 13, 12) orbits: { 1, 7, 8, 5, 6, 4, 3, 2 }, { 9, 12, 11, 10, 16, 17, 15, 14, 13 }, { 18 } code no 2: ================ 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 the automorphism group has order 3657830400 and is strongly generated by the following 25 elements: ( 1 0 0 0 0 0 0 0 0 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14, 16), (12, 14, 16, 13, 15), (11, 15, 12, 16), (10, 14, 16, 15, 12, 11, 13), (9, 10, 14)(11, 16)(12, 15), (9, 16, 12, 14, 10, 15, 13), (9, 13, 12, 10, 11, 14, 15, 16, 18), (8, 17)(9, 16, 12, 10, 15, 13, 11, 14), (7, 17, 8)(9, 16, 15)(10, 14, 12)(11, 13), (6, 17)(9, 10, 12, 16)(11, 14, 15), (6, 17, 7, 8)(9, 16, 11, 14)(10, 15, 12, 13), (5, 17)(9, 11, 14)(10, 15, 13, 12), (5, 6, 8, 17, 7)(9, 11, 13)(10, 14, 16)(12, 15), (4, 6, 8, 5)(9, 12, 11, 16, 14)(10, 13), (4, 8, 7)(5, 17, 6)(10, 16, 11, 12), (3, 7)(4, 5)(9, 14, 10)(11, 15, 16, 12), (3, 7, 5)(4, 8, 17)(9, 16, 11)(13, 14), (1, 2)(3, 7)(5, 6, 17, 8)(9, 12, 14, 11)(13, 16) orbits: { 1, 2 }, { 3, 7, 5, 8, 17, 6, 4 }, { 9, 14, 13, 18, 15, 16, 10, 11, 12 } code no 3: ================ 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 the automorphism group has order 1567641600 and is strongly generated by the following 21 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 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(7, 17)(9, 16)(10, 14, 12, 13)(11, 15), (7, 8)(9, 11, 14, 12, 13, 16, 10), (6, 7)(9, 11, 10, 16, 14, 13), (6, 7, 17, 8)(10, 13, 12, 16)(11, 14), (5, 6)(7, 8)(9, 12, 10, 14, 16, 11), (4, 17, 7, 6)(9, 14)(11, 13)(12, 16), (4, 6, 8, 5)(9, 13)(11, 15, 14, 16, 12), (2, 3)(4, 6)(5, 7)(9, 12, 11, 14, 15, 13, 16), (1, 2)(4, 5)(6, 8)(9, 11)(10, 13, 14, 12, 16) orbits: { 1, 2, 3 }, { 4, 6, 5, 7, 8, 17 }, { 9, 16, 11, 18, 10, 13, 14, 15, 12 } code no 4: ================ 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 the automorphism group has order 1045094400 and is strongly generated by the following 17 elements: ( 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 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0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 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 0 , 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (16, 18), (15, 16), (14, 16, 15), (13, 16, 14), (12, 15, 16, 13, 14), (11, 15)(12, 16, 14, 13), (10, 12, 11, 16)(13, 14), (9, 12, 16, 13, 11, 10, 14), (9, 10, 15, 18)(11, 13), (8, 17)(9, 12, 15, 14, 13, 11, 10), (7, 17)(9, 13)(10, 11, 16, 14), (7, 8)(9, 12, 13, 11)(10, 15, 16), (6, 8, 7)(9, 14, 16, 15, 10)(12, 13), (5, 8, 7)(9, 15, 16, 12, 11, 10)(13, 14), (3, 4)(9, 16, 11, 15)(10, 12, 13), (2, 4, 3)(5, 8, 6)(9, 16, 12)(11, 14, 15), (1, 4, 3, 2)(5, 7, 6)(9, 13, 11, 10, 15, 12, 14) orbits: { 1, 2, 3, 4 }, { 5, 7, 6, 17, 8 }, { 9, 14, 18, 10, 13, 11, 15, 12, 16 }