the 1 isometry classes of irreducible [15,11,4]_4 codes are: code no 1: ================ 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 1 0 0 0 0 0 0 0 0 2 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 2 0 1 0 0 0 0 1 0 0 0 0 0 0 3 2 1 1 0 0 0 0 0 1 0 0 0 0 0 2 3 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 1 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 0 0 3 3 2 1 0 0 0 0 0 0 0 0 0 1 0 3 0 3 1 0 0 0 0 0 0 0 0 0 0 1 the automorphism group has order 120 and is strongly generated by the following 5 elements: ( 2 0 0 0 0 1 0 0 0 2 1 2 3 1 1 0 , 1 , 2 0 0 0 1 0 1 2 1 1 1 1 2 1 3 3 , 0 , 0 3 0 0 2 0 0 0 2 1 1 0 2 1 0 1 , 0 , 1 0 1 3 0 1 0 0 1 2 3 3 3 1 1 0 , 1 , 3 3 3 3 2 1 0 2 0 0 3 0 1 0 1 3 , 1 ) acting on the columns of the generator matrix as follows (in order): (3, 8, 5, 13)(4, 11, 14, 6)(7, 9, 10, 12), (2, 15)(3, 5)(4, 10)(6, 9)(7, 14)(8, 13)(11, 12), (1, 2)(3, 6)(4, 8)(5, 11)(13, 14), (1, 15)(3, 7, 5, 10)(4, 11, 14, 6)(8, 9, 13, 12), (1, 8, 13, 5)(2, 7, 14, 9)(4, 10, 11, 15)(6, 12) orbits: { 1, 2, 15, 5, 9, 11, 8, 3, 7, 13, 6, 14, 4, 12, 10 }