the 4 isometry classes of irreducible [17,2,8]_2 codes are: code no 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 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 1828915200 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 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 1 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 1 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 1 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 1 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 1 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(11, 16, 12, 13, 15, 14), (10, 16, 14, 13, 15, 12, 11), (9, 10, 11, 14, 12, 13, 16, 15), (8, 9), (8, 10, 11, 15, 12, 14, 13, 9, 16), (6, 7)(8, 11, 13)(9, 15, 14, 10, 16, 12), (5, 6)(8, 13, 10, 15)(9, 12, 16, 11, 14), (5, 7)(9, 11, 14)(10, 12), (4, 5, 7)(8, 10, 12, 14, 11, 9), (3, 6, 5)(4, 7)(8, 9, 11, 13, 15)(10, 16, 12), (2, 5)(4, 6)(9, 10, 15, 11, 14, 12, 16), (1, 4, 6, 3, 7, 5, 2)(8, 15, 12, 11)(10, 16, 13) orbits: { 1, 2, 5, 6, 7, 4, 3 }, { 8, 9, 16, 13, 15, 11, 12, 14, 10 }, { 17 } code no 2: ================ 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 the automorphism group has order 522547200 and is strongly generated by the following 24 elements: ( 1 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 1 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 1 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 1 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 1 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 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7)(8, 11, 14, 10, 9, 13, 15), (3, 6, 4, 7, 5)(8, 11)(10, 12, 14, 15), (1, 2)(3, 6)(8, 14, 10, 9, 11, 13, 15) orbits: { 1, 2 }, { 3, 5, 6, 16, 7, 4 }, { 8, 12, 11, 13, 17, 10, 9, 15, 14 } code no 3: ================ 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 the automorphism group has order 261273600 and is strongly generated by the following 24 elements: ( 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 , 1 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 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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 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ) acting on the columns of the generator matrix as follows (in order): (15, 17), (14, 15), (14, 15, 17), (13, 14), (13, 14, 15), (12, 13, 15), (11, 13), (11, 13, 14), (11, 15, 13, 17)(12, 14), (10, 15), (10, 15, 14), (10, 12, 13, 17), (9, 15, 10)(11, 13, 14), (9, 12), (8, 15)(9, 11), (8, 15, 11, 12)(9, 13)(10, 14), (8, 12, 15, 10, 14, 11, 17)(9, 13), (7, 16)(8, 12)(9, 11, 15, 13, 10, 14), (6, 16, 7)(8, 11, 12, 10)(9, 13, 14, 15), (5, 7)(6, 16)(8, 11, 10, 9, 12, 14, 15, 13), (5, 6)(9, 13, 14, 11, 10, 15, 12), (4, 5, 6, 7)(8, 15, 14, 10, 11, 9, 12, 13), (2, 3)(4, 6, 16)(5, 7)(8, 11, 14)(9, 10, 15), (1, 2, 3)(4, 7, 16, 5, 6)(8, 10)(9, 13, 15, 14, 12) orbits: { 1, 3, 2 }, { 4, 7, 16, 6, 5 }, { 8, 15, 12, 17, 10, 13, 14, 11, 9 } code no 4: ================ 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 the automorphism group has order 418037760 and is strongly generated by the following 22 elements: ( 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 , 1 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 1 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 1 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 1 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 1 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 1 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 1 0 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0 1 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 1 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (15, 17), (14, 15), (14, 15, 17), (13, 14, 15), (12, 14), (12, 14, 13, 15, 17), (11, 13), (11, 13, 12)(14, 15), (10, 12), (10, 11), (10, 13, 12, 15)(11, 14), (9, 12), (9, 12, 10, 15), (8, 12, 13)(9, 15, 11, 14), (8, 12, 17)(9, 15, 10, 11, 14, 13), (7, 16)(8, 13, 9, 15, 14, 11)(10, 12), (6, 7)(8, 14, 15, 13, 11, 12, 9, 10), (5, 6, 7, 16)(8, 15, 9)(10, 12, 14, 13, 11), (3, 4)(6, 7)(8, 13, 11)(9, 12)(10, 14), (2, 4, 3)(6, 16)(8, 11, 12, 14)(9, 15, 13), (1, 6)(2, 16, 4, 5, 3, 7)(8, 13, 15)(9, 10)(11, 14, 12), (1, 7)(2, 6, 3, 5)(4, 16)(8, 13)(9, 11, 12, 14, 10, 15) orbits: { 1, 6, 7, 5, 16, 2, 3, 4 }, { 8, 13, 17, 11, 10, 9, 14, 15, 12 }