the 4 isometry classes of irreducible [16,2,8]_2 codes are: code no 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 1 the automorphism group has order 203212800 and is strongly generated by the following 14 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 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 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 1 1 1 1 1 1 1 1 1 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14, 12), (5, 7)(8, 9, 12, 10)(13, 14, 15), (4, 7, 6, 5)(8, 13)(9, 10, 15)(11, 12, 14), (3, 7, 6)(8, 14, 15)(9, 11, 12), (2, 5)(3, 6, 7)(8, 15, 14)(9, 12, 11), (2, 4, 7, 3, 6)(8, 11, 10, 9, 12)(13, 15), (1, 3, 7, 6, 4)(9, 15, 11) orbits: { 1, 4, 5, 2, 6, 7, 3 }, { 8, 11, 12, 10, 13, 15, 14, 9 }, { 16 } code no 2: ================ 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 the automorphism group has order 58060800 and is strongly generated by the following 22 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 0 0 0 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 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 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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 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 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (14, 16), (13, 14), (12, 13), (11, 14), (11, 14, 13), (11, 13, 12), (11, 16), (10, 11)(13, 14), (10, 13, 11, 14, 12, 16), (9, 14, 11)(10, 13), (9, 13, 10), (9, 13, 11, 12), (9, 14, 16)(10, 12, 13), (8, 9, 14, 13), (8, 12, 16)(10, 13, 11), (7, 15)(8, 9, 11, 10, 14, 12), (6, 7, 15)(8, 11, 14, 12)(9, 13, 10), (5, 15, 6, 7)(8, 10, 13, 12, 9, 11), (4, 6, 15)(8, 9, 12, 11, 14)(10, 13), (4, 6, 7, 15, 5)(8, 12, 14, 13, 9, 10), (3, 7, 6, 4, 5)(8, 11, 14)(9, 12, 10), (1, 2)(3, 4, 7, 6)(8, 9)(10, 14, 13) orbits: { 1, 2 }, { 3, 5, 6, 7, 15, 4 }, { 8, 13, 16, 12, 11, 14, 10, 9 } code no 3: ================ 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 the automorphism group has order 29030400 and is strongly generated by the following 22 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 1 0 0 0 0 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 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 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 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11), (5, 15)(6, 7)(8, 13, 12, 9, 11)(10, 14), (4, 5)(6, 7)(8, 9)(11, 13), (4, 6, 7)(8, 9, 12, 14, 13)(10, 11), (4, 5, 7, 15)(10, 13, 11, 14, 12), (2, 3)(4, 7, 5, 6)(8, 11, 9, 13), (1, 3, 2)(4, 15, 5)(8, 9, 14, 13, 10, 12, 11) orbits: { 1, 2, 3 }, { 4, 5, 7, 15, 6 }, { 8, 12, 16, 13, 11, 9, 10, 14 } code no 4: ================ 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 the automorphism group has order 46448640 and is strongly generated by the following 21 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 1 1 0 0 0 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 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 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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 1 0 0 0 0 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 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 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 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 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 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 1 1 1 1 1 1 1 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 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 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 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 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): (14, 16), (13, 14), (13, 14, 16), (12, 14), (12, 13), (12, 16), (11, 14, 13), (11, 13, 14, 12), (10, 13)(12, 14), (10, 16)(12, 13), (9, 13, 10)(12, 14), (8, 9)(10, 14)(11, 12), (8, 12, 16)(9, 13, 14, 11, 10), (7, 15)(8, 9, 14, 12)(10, 13), (6, 15, 7)(8, 11, 9)(10, 14, 12, 13), (5, 7)(6, 15)(8, 11)(9, 13), (5, 15)(8, 9, 10, 14, 13, 11, 12), (3, 4)(5, 15, 7, 6)(8, 9, 12, 11)(10, 13), (2, 4)(5, 7)(8, 9, 11)(10, 12, 13), (1, 2, 3)(5, 15)(6, 7)(8, 13, 11, 14, 10, 12), (1, 7, 3, 15, 4, 5)(2, 6)(8, 12, 14, 10, 13)(9, 11) orbits: { 1, 3, 5, 4, 2, 7, 15, 6 }, { 8, 9, 16, 12, 11, 13, 10, 14 }