the 2 isometry classes of irreducible [17,3,9]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 the automorphism group has order 20736 and is strongly generated by the following 12 elements: ( 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 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 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 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 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 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 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 , 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 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 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 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 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 0 1 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (14, 17), (13, 14), (13, 14, 17), (12, 16)(13, 14), (11, 12, 16), (9, 10)(11, 16), (8, 15)(11, 16), (7, 15)(12, 16), (5, 9)(6, 10)(7, 16, 8, 11)(12, 15)(13, 14), (3, 4)(5, 6)(7, 15, 8)(9, 10)(11, 12), (3, 9)(4, 10)(5, 6)(7, 13, 8, 14, 15, 17)(11, 16, 12), (1, 2)(5, 6)(7, 8)(11, 16, 12) orbits: { 1, 2 }, { 3, 4, 9, 10, 5, 6 }, { 7, 15, 11, 8, 17, 12, 14, 16, 13 } code no 2: ================ 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 the automorphism group has order 41472 and is strongly generated by the following 13 elements: ( 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 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 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 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 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 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0 1 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 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 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 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 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 1 0 0 0 1 1 1 1 0 0 0 0 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 1 0 , 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 1 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 1 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 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (14, 17), (13, 14), (12, 16), (11, 16, 12), (9, 10), (8, 15)(9, 10), (7, 15)(12, 16), (7, 8)(11, 16, 12)(13, 14), (5, 6)(7, 15, 8)(11, 16)(13, 14), (5, 9)(6, 10)(7, 11, 15, 16, 8, 12), (2, 3)(11, 12)(13, 14), (1, 3, 2)(5, 6)(7, 8)(9, 10)(12, 16)(13, 14), (1, 16, 2, 12, 3, 11)(5, 6)(7, 14, 15, 13, 8, 17) orbits: { 1, 2, 11, 3, 16, 12, 7, 15, 8, 17, 14, 13 }, { 4 }, { 5, 6, 9, 10 }