the 6 isometry classes of irreducible [19,3,10]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 the automorphism group has order 7962624 and is strongly generated by the following 20 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 0 1 0 0 0 1 0 0 0 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 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17, 8, 9)(11, 18, 12)(14, 16, 15), (2, 4)(6, 10)(7, 13, 8, 12, 9, 18)(11, 17)(15, 16), (2, 4, 3)(7, 8)(9, 17)(12, 13), (1, 9, 13, 4, 7, 12, 3, 17, 18)(2, 8, 11)(5, 6, 10)(14, 16, 15), (1, 13, 9, 15, 2, 11, 7, 16, 4, 12, 8, 14, 3, 18, 17, 19)(5, 6) orbits: { 1, 18, 19, 13, 12, 11, 9, 17, 3, 16, 15, 7, 8, 4, 14, 2 }, { 5, 10, 6 } code no 2: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 the automorphism group has order 331776 and is strongly generated by the following 16 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 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(9, 17)(11, 18)(14, 15), (8, 17, 9)(11, 13, 12)(14, 15, 16), (6, 7)(9, 17)(11, 12, 13)(14, 15, 16), (4, 5), (4, 6)(5, 7)(8, 9, 17)(11, 19)(12, 14, 13, 15)(16, 18), (2, 3)(6, 7)(8, 17, 9)(11, 12, 18, 13)(14, 15), (1, 2, 3)(4, 5)(6, 7)(8, 9, 17)(11, 18, 12)(14, 16, 15), (1, 17)(2, 8)(3, 9)(4, 6)(5, 7)(12, 18)(14, 16) orbits: { 1, 3, 17, 2, 9, 8 }, { 4, 5, 6, 7 }, { 10 }, { 11, 12, 13, 18, 19, 15, 14, 16 } code no 3: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 the automorphism group has order 248832 and is strongly generated by the following 16 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 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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 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 1 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 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 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 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 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 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 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 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 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 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (16, 19), (15, 16), (15, 16, 19), (14, 15, 16), (14, 19)(15, 16), (13, 18)(14, 16, 15), (12, 18, 13)(14, 16), (10, 11)(12, 13)(14, 15), (9, 17)(15, 16), (8, 17, 9)(10, 11)(12, 13)(15, 16), (6, 10)(7, 11)(8, 12)(9, 18)(13, 17)(14, 16, 15), (6, 7)(8, 9, 17)(12, 13, 18)(14, 16), (4, 5)(14, 16, 15), (3, 4), (1, 2)(3, 4, 5)(6, 7)(13, 18)(14, 16), (1, 6, 2, 7)(3, 17)(4, 8, 5, 9)(10, 11)(12, 13)(14, 15) orbits: { 1, 2, 7, 6, 11, 10 }, { 3, 4, 5, 17, 9, 8, 13, 18, 12 }, { 14, 16, 19, 15 } code no 4: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 the automorphism group has order 248832 and is strongly generated by the following 15 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 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1 0 0 1 1 1 0 0 1 1 0 0 1 the automorphism group has order 1119744 and is strongly generated by the following 16 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 0 0 0 1 1 1 0 0 1 1 1 0 0 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 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 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 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 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 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 ) acting on the columns of the generator matrix as follows (in order): (16, 19), (15, 16), (15, 16, 19), (14, 18), (13, 14)(15, 16), (11, 12), (10, 11, 12)(14, 18)(15, 16), (9, 17)(10, 11)(15, 16), (8, 9, 17)(10, 12, 11)(15, 16), (6, 7)(8, 9, 17)(13, 14)(15, 16), (5, 9, 7, 8, 6, 17)(10, 14)(11, 18)(12, 13)(15, 16), (5, 14, 6, 18)(7, 13)(8, 11, 9, 10)(12, 17)(15, 16), (3, 4)(5, 17, 6, 8)(7, 9)(10, 14)(11, 18)(12, 13)(15, 16), (2, 3)(5, 10, 7, 12)(6, 11)(8, 13, 17, 14, 9, 18)(15, 16), (2, 3, 4)(5, 17)(6, 8)(7, 9)(10, 14, 11, 18, 12, 13), (2, 13, 8)(3, 14, 9, 4, 18, 17)(5, 11, 19)(6, 12, 15)(7, 10, 16) orbits: { 1 }, { 2, 3, 4, 8, 17, 9, 7, 10, 6, 18, 13, 12, 5, 11, 14, 16, 15, 19 } code no 6: ================ 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 the automorphism group has order 248832 and is strongly generated by the following 14 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 0 0 1 1 1 0 0 1 1 1 0 0 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 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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 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 1 1 1 1 1 1 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 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 1 1 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 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 ) acting on the columns of the generator matrix as follows (in order): (16, 19), (15, 16), (15, 16, 19), (14, 18)(15, 16), (13, 18), (11, 12)(15, 16), (10, 11, 12)(13, 18, 14), (9, 17)(14, 18)(15, 16), (8, 9, 17), (6, 7), (5, 10)(6, 11, 7, 12)(8, 13, 9, 14)(15, 16)(17, 18), (5, 14)(6, 13, 7, 18)(8, 11)(9, 12, 17, 10)(15, 16), (3, 4)(8, 17)(10, 11)(13, 14)(15, 16), (1, 4, 2, 3)(6, 7)(8, 9, 17)(10, 14)(11, 18)(12, 13) orbits: { 1, 3, 4, 2 }, { 5, 10, 14, 12, 17, 11, 18, 9, 13, 7, 8, 6 }, { 15, 16, 19 }