Some designs and codes from L_2(q)

For q in {7,8,9,11,13,16}, we consider the primitive actions of L2(q) and use Key-Moori Method 1 as described in [5, 6] to construct designs from the orbits of the point stabilisers and from any union of these orbits. We also use Key-Moori Method 2 (see [8]) to determine the designs from the maximal subgroups and the conjugacy classes of elements of these groups. The incidence matrices of these designs are then used to generate associated binary codes. The full automorphisms of these designs and codes are also determined.