the 6 isometry classes of irreducible [14,5,6]_2 codes are: code no 1: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 1 the automorphism group has order 24 and is strongly generated by the following 4 elements: ( 1 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 1 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 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 , 1 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 , 1 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 1 0 0 0 0 0 0 0 1 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 1 0 1 1 1 1 1 1 1 1 1 , 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (9, 10), (4, 6)(5, 7)(11, 12), (2, 3)(4, 7)(5, 6)(9, 10)(11, 12)(13, 14), (1, 12)(2, 3)(4, 13)(5, 14)(6, 7) orbits: { 1, 12, 11 }, { 2, 3 }, { 4, 6, 7, 13, 5, 14 }, { 8 }, { 9, 10 } code no 2: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 4 elements: ( 1 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 , 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 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 , 1 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 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 , 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 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): (4, 6)(5, 7)(11, 12), (3, 6)(5, 8)(11, 13), (2, 6, 3, 4)(5, 8, 7, 9)(11, 13, 12, 14), (1, 10)(2, 9)(3, 8)(4, 5)(6, 7)(11, 12) orbits: { 1, 10 }, { 2, 4, 9, 6, 3, 5, 7, 8 }, { 11, 12, 13, 14 } code no 3: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 the automorphism group has order 16 and is strongly generated by the following 4 elements: ( 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 , 1 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 1 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 0 0 0 0 1 0 0 0 0 0 0 0 1 0 , 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 , 1 1 1 0 0 1 1 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 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 ) acting on the columns of the generator matrix as follows (in order): (2, 14)(3, 13)(4, 9)(5, 8)(10, 12), (2, 3)(4, 5)(8, 9)(13, 14), (1, 10)(2, 9)(3, 8)(4, 5)(6, 7)(11, 12), (1, 10, 11, 12)(2, 13, 9, 4, 3, 14, 8, 5)(6, 7) orbits: { 1, 10, 12, 11 }, { 2, 14, 3, 9, 5, 13, 8, 4 }, { 6, 7 } code no 4: ================ 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 the automorphism group has order 96 and is strongly generated by the following 5 elements: ( 1 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 1 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 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 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 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 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 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 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 1 0 0 0 0 0 0 0 1 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 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 , 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 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 1 ) acting on the columns of the generator matrix as follows (in order): (9, 10), (2, 4)(3, 5)(7, 8)(9, 10)(12, 13), (2, 8)(3, 12)(4, 7)(5, 13)(6, 14), (1, 11)(2, 5)(3, 4)(7, 12)(8, 13)(9, 10), (1, 7, 12, 11, 5, 2)(3, 13, 6, 8, 4, 14) orbits: { 1, 11, 2, 12, 4, 8, 5, 13, 3, 7, 6, 14 }, { 9, 10 } code no 5: ================ 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 the automorphism group has order 1152 and is strongly generated by the following 7 elements: ( 1 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 1 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 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 , 1 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 , 1 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 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 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 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 0 0 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 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 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 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 ) acting on the columns of the generator matrix as follows (in order): (9, 14), (4, 6)(5, 7)(10, 11), (3, 6, 4)(5, 7, 12)(8, 10, 11), (2, 7)(4, 13)(8, 10), (2, 6, 7, 13, 5, 4)(3, 12)(8, 11, 10), (1, 5, 3)(2, 13, 10, 7, 4, 8)(6, 11, 12), (1, 7)(2, 11)(3, 6)(5, 10)(8, 12) orbits: { 1, 3, 7, 4, 12, 5, 6, 2, 10, 13, 11, 8 }, { 9, 14 } code no 6: ================ 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 the automorphism group has order 2688 and is strongly generated by the following 9 elements: ( 1 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 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 , 1 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 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 1 1 0 , 1 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 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 , 1 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 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 1 0 1 , 1 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 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 , 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 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 , 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 0 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 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 1 0 0 0 , 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 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 1 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 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 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 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 ) acting on the columns of the generator matrix as follows (in order): (6, 12)(7, 9)(8, 14)(11, 13), (6, 14)(7, 13)(8, 12)(9, 11), (6, 11)(7, 8)(9, 14)(12, 13), (5, 10)(8, 11)(9, 12), (3, 5)(4, 10)(6, 8)(7, 11), (3, 8)(4, 11)(5, 6)(7, 10), (3, 6, 9)(4, 7, 12)(5, 8, 13)(10, 11, 14), (1, 7, 11, 2, 6, 8)(3, 12, 10)(4, 9, 5), (1, 9, 14)(2, 12, 13)(3, 4)(5, 7, 11, 10, 6, 8) orbits: { 1, 8, 14, 12, 7, 11, 6, 3, 5, 9, 13, 2, 10, 4 }