A construction of mutually disjoint Steiner systems from isomorphic Golay codes

It is well known that the extended binary Golay [ 24 , 12 , 8 ] code yields 5-designs. In particular, the supports of all the weight 8 codewords in the code form a Steiner system S ( 5 , 8 , 24 ) . In this paper, we give a construction of mutually disjoint Steiner systems S ( 5 , 8 , 24 ) by constructing isomorphic Golay codes. As a consequence, we show that there exists at least 22 mutually disjoint Steiner systems S ( 5 , 8 , 24 ) . Finally, we prove that there exists at least 46 mutually disjoint 5 - ( 48 , 12 , 8 ) designs from the extended binary quadratic residue [ 48 , 24 , 12 ] code.