Constructions for strictly cyclic 3-designs and applications to optimal OOCs with

In this paper we give some recursive constructions for strictly cyclic 3-designs. Using these constructions we have some infinite families of strictly cyclic Steiner quadruple systems and optimal optical orthogonal codes with weight 4 and index 2. As corollaries, many known constructions for strictly cyclic Steiner quadruple systems and optimal optical orthogonal codes are unified. We also notice that there does not exist an optimal ( n , 4 , 2 ) -OOC for any n ≡ 0 ( mod 24 ). Thus we introduce the concept of strictly cyclic maximal packing quadruple systems to deal with the cases of n ≡ 0 ( mod 24 ) for ( n , 4 , 2 ) -OOCs. By our recursive constructions, some infinite families are also given on strictly cyclic maximal packing quadruple systems.