the 2 isometry classes of irreducible [19,2,12]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 the automorphism group has order 6096384000 and is strongly generated by the following 25 elements: ( 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 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 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 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 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 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 , 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 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 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(11, 18)(12, 13)(14, 16, 15, 17), (10, 11)(12, 15, 13, 14, 16), (9, 10)(11, 18)(12, 15)(13, 16), (9, 11)(12, 14, 13, 15, 17), (8, 9)(10, 18, 11)(12, 16, 14, 13)(15, 17), (7, 10, 11, 18, 9, 8)(12, 16, 15, 14, 17), (6, 10, 18, 8)(12, 17, 13, 15), (6, 9)(7, 10, 18, 11)(12, 15, 14, 16)(13, 17), (6, 17, 7, 14, 9, 19)(8, 16)(10, 12, 11, 15, 18, 13), (4, 5)(6, 7, 18, 10, 8)(12, 14, 17, 15, 13, 16), (3, 5, 4)(8, 10, 18, 11)(12, 14, 17), (2, 3, 4)(6, 9)(12, 15, 16, 17, 13), (1, 5, 3, 4, 2)(8, 18)(9, 11)(12, 13, 15, 14, 16, 17) orbits: { 1, 2, 4, 5, 3 }, { 6, 8, 9, 19, 18, 16, 10, 11, 14, 17, 13, 15, 7, 12 } code no 2: ================ 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1 the automorphism group has order 5225472000 and is strongly generated by the following 23 elements: ( 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 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 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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 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 1 0 ) acting on the columns of the generator matrix as follows (in order): (17, 19), (16, 17), (15, 17, 16), (14, 17)(15, 16), (13, 15), (13, 16)(14, 17), (13, 17, 14)(15, 16), (12, 16)(13, 14), (12, 17, 19)(13, 16, 14), (11, 18)(12, 13, 16), (10, 11)(12, 17, 14, 16)(13, 15), (10, 11, 18)(12, 13, 17, 15, 16), (9, 18)(13, 15, 16)(14, 17), (9, 11)(10, 18)(12, 14, 16, 13, 17), (8, 10, 9, 11)(12, 16, 17)(13, 14, 15), (7, 10)(8, 18)(9, 11)(12, 13, 14, 17, 15), (7, 18)(8, 10, 9, 11)(12, 13, 17, 14, 16, 15), (5, 6)(7, 11, 18)(12, 17, 16, 14, 13), (4, 6)(7, 18, 8)(9, 10)(12, 16, 14), (4, 5)(7, 9, 11, 10)(12, 13, 14, 16), (3, 6)(4, 5)(7, 18, 9, 10, 8)(12, 15)(13, 17, 14), (2, 6, 5)(7, 9, 18, 10)(8, 11)(12, 16, 15)(13, 17), (1, 9, 2, 8, 5, 7, 3, 10, 6, 11, 4, 18)(13, 15, 16, 17) orbits: { 1, 18, 11, 9, 10, 8, 7, 4, 6, 3, 2, 5 }, { 12, 16, 19, 17, 15, 13, 14 }