the 3 isometry classes of irreducible [15,2,7]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 29030400 and is strongly generated by the following 17 elements: ( 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 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 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 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 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 1 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 0 0 0 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 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 1 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (13, 14), (12, 13), (12, 13, 14), (11, 12)(13, 14), (11, 14, 13), (10, 12, 13, 11, 14), (9, 12, 14, 10)(11, 13), (8, 12)(10, 14), (8, 10)(13, 14), (7, 11)(8, 10, 12, 14), (7, 13)(9, 11), (5, 6)(7, 8, 10, 9, 14, 13, 11), (4, 6, 5)(7, 14, 12, 10, 8, 9, 11), (3, 5, 4, 6)(7, 11, 10, 14, 12, 13)(8, 9), (2, 5)(4, 6)(7, 11, 8, 12)(9, 10), (2, 3)(4, 5)(7, 13, 8, 10)(9, 11, 12, 14), (1, 4, 2, 5, 3)(7, 8)(9, 12, 10, 13) orbits: { 1, 3, 6, 2, 5, 4 }, { 7, 11, 13, 12, 10, 8, 9, 14 }, { 15 } code no 2: ================ 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 the automorphism group has order 9676800 and is strongly generated by the following 20 elements: ( 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 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 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 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 1 0 0 0 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1 0 0 0 0 0 0 0 0 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 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 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 1 0 0 0 0 0 0 0 0 0 1 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 1 1 1 1 1 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 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 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 1 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): (13, 15), (12, 13), (12, 13, 15), (11, 12, 13), (11, 15)(12, 13), (10, 11, 12), (10, 13, 11, 12, 15), (9, 13)(10, 12, 11), (9, 13, 12), (8, 13)(9, 11, 10, 12), (7, 9, 8, 10), (7, 12, 9, 13, 8, 10, 11), (7, 11, 15)(8, 10, 9, 13), (6, 14)(8, 9)(10, 11, 12, 13), (5, 14)(7, 9, 8, 11, 13, 10, 12), (4, 14)(7, 8, 12, 10, 9, 11, 13), (4, 5)(7, 8, 11)(9, 12, 13), (3, 14, 4)(7, 12, 8)(9, 10, 13, 11), (3, 14, 6)(8, 9, 11, 10, 13, 12), (1, 2)(3, 14)(4, 5)(7, 13)(8, 10, 12, 11) orbits: { 1, 2 }, { 3, 4, 6, 14, 5 }, { 7, 10, 11, 15, 12, 13, 8, 9 } code no 3: ================ 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 the automorphism group has order 5806080 and is strongly generated by the following 20 elements: ( 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 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 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 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 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 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 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 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 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