the 4 isometry classes of irreducible [13,9,4]_4 codes are: code no 1: ================ 1 1 1 1 1 0 0 0 0 0 0 0 0 2 1 1 0 0 1 0 0 0 0 0 0 0 1 2 1 0 0 0 1 0 0 0 0 0 0 3 3 1 0 0 0 0 1 0 0 0 0 0 2 1 0 1 0 0 0 0 1 0 0 0 0 1 2 0 1 0 0 0 0 0 1 0 0 0 3 3 0 1 0 0 0 0 0 0 1 0 0 2 0 1 1 0 0 0 0 0 0 0 1 0 0 2 1 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 48 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 3 0 0 0 0 1 0 2 1 0 1 , 0 , 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 , 0 , 1 0 0 0 0 1 0 0 3 3 1 0 3 3 0 1 , 0 , 1 0 0 0 0 1 0 0 1 2 0 1 1 2 1 0 , 0 , 0 3 0 0 1 0 0 0 2 3 2 0 0 0 0 2 , 0 ) acting on the columns of the generator matrix as follows (in order): (4, 10, 9)(5, 12, 13)(6, 7, 8), (3, 4)(6, 9)(7, 10)(8, 11), (3, 8)(4, 11)(6, 7)(9, 10), (3, 10)(4, 7)(6, 11)(8, 9), (1, 2)(3, 7)(5, 12)(9, 11) orbits: { 1, 2 }, { 3, 4, 8, 10, 7, 9, 11, 6 }, { 5, 13, 12 } code no 2: ================ 1 1 1 1 1 0 0 0 0 0 0 0 0 2 1 1 0 0 1 0 0 0 0 0 0 0 1 2 1 0 0 0 1 0 0 0 0 0 0 3 3 1 0 0 0 0 1 0 0 0 0 0 2 1 0 1 0 0 0 0 1 0 0 0 0 1 2 0 1 0 0 0 0 0 1 0 0 0 3 3 0 1 0 0 0 0 0 0 1 0 0 3 0 1 1 0 0 0 0 0 0 0 1 0 2 2 1 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 192 and is strongly generated by the following 6 elements: ( 1 0 0 0 0 1 0 0 0 0 2 0 0 0 0 2 , 1 , 1 0 0 0 0 1 0 0 3 3 0 1 3 3 1 0 , 0 , 1 0 0 0 0 1 0 0 3 3 1 0 3 3 0 1 , 0 , 1 0 0 0 0 1 0 0 1 2 0 1 1 2 1 0 , 0 , 0 2 0 0 2 0 0 0 1 1 3 0 0 0 0 3 , 1 , 1 3 1 0 3 1 1 0 0 1 0 0 2 3 0 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (5, 13)(6, 7)(9, 10), (3, 11)(4, 8)(6, 10)(7, 9), (3, 8)(4, 11)(6, 7)(9, 10), (3, 10)(4, 7)(6, 11)(8, 9), (1, 2)(3, 8)(6, 7), (1, 8, 6, 2, 3, 7)(4, 5, 9)(10, 11, 13) orbits: { 1, 2, 7, 6, 9, 4, 3, 10, 11, 8, 5, 13 }, { 12 } code no 3: ================ 1 1 1 1 1 0 0 0 0 0 0 0 0 2 1 1 0 0 1 0 0 0 0 0 0 0 1 2 1 0 0 0 1 0 0 0 0 0 0 2 1 0 1 0 0 0 1 0 0 0 0 0 1 2 0 1 0 0 0 0 1 0 0 0 0 3 2 1 1 0 0 0 0 0 1 0 0 0 2 3 1 1 0 0 0 0 0 0 1 0 0 1 0 2 1 0 0 0 0 0 0 0 1 0 0 1 2 1 0 0 0 0 0 0 0 0 1 the automorphism group has order 8 and is strongly generated by the following 2 elements: ( 0 3 1 3 2 1 3 3 0 0 2 0 3 1 0 3 , 0 , 3 2 1 1 0 1 2 1 0 0 3 0 1 2 0 1 , 0 ) acting on the columns of the generator matrix as follows (in order): (1, 13)(2, 10)(4, 9)(5, 8)(6, 12)(7, 11), (1, 12, 7, 10)(2, 11, 6, 13)(4, 8, 5, 9) orbits: { 1, 13, 10, 6, 2, 7, 12, 11 }, { 3 }, { 4, 9, 5, 8 } code no 4: ================ 1 1 1 1 1 0 0 0 0 0 0 0 0 2 1 1 0 0 1 0 0 0 0 0 0 0 1 2 1 0 0 0 1 0 0 0 0 0 0 2 1 0 1 0 0 0 1 0 0 0 0 0 1 2 0 1 0 0 0 0 1 0 0 0 0 3 2 1 1 0 0 0 0 0 1 0 0 0 2 3 1 1 0 0 0 0 0 0 1 0 0 1 0 2 1 0 0 0 0 0 0 0 1 0 3 0 3 1 0 0 0 0 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 1 0 0 0 0 0 1 0 0 1 0 , 0 , 2 0 0 0 1 3 2 2 3 0 2 3 3 0 3 2 , 1 , 0 0 0 2 2 3 0 3 1 1 1 1 0 3 0 0 , 1 , 3 0 3 2 1 0 3 1 1 2 2 0 0 0 2 0 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 4)(6, 8)(7, 9)(12, 13), (2, 11)(3, 13, 4, 12)(6, 7, 8, 9), (1, 8, 2, 4)(3, 11, 6, 5)(7, 12), (1, 9, 5, 13)(2, 7, 11, 12)(3, 4, 8, 6) orbits: { 1, 4, 13, 3, 2, 12, 5, 6, 11, 8, 7, 9 }, { 10 }