A t-(v, k, λ) design D is a pair of a set X of v points and a collection B of k-subsets of X called blocks such that every t-subset of X is contained in exactly λ blocks. We often denote the design D by (X, B ). A design with no repeated block is called simple. All designs in this note are simple. A Steiner system S(t, k, v) is a t-(v, k, λ) design with λ = 1. Two t-(v, k, λ) designs with the same point set are said to be disjoint if they have no blocks in common. Two t-(v, k, λ) designs are isomorphic if there is a bijection between their point sets that maps the blocks of the first design into the blocks of the second design. An automorphism of a t-(v, k, λ) design D is any isomorphism of the design with itself and the set consisting of all automorphisms of D is called the automorphism group Aut(D) of D. The well-known Steiner system S(5, 8, 24) and a 5-(24, 12, 48) design are constructed by taking as blocks the supports of codewords of weights 8 and 12 in the extended Go- lay [24, 12, 8] code, respectively. It is well known that there is a unique Steiner system S(5, 8, 24) up to isomorphism [8], and there is a unique 5-(24, 12, 48) design having even