Some series of optimal multilength OOCs of weight four

Two cyclic relative difference families (n,g,w,1)(n,g,w,1)-CRDFs AA and BB are called 2-compatible if |(A+x)∩(B+y)|≤2|(A+x)∩(B+y)|≤2 for any A∈AA∈A, B∈BB∈B and x,y∈Znx,y∈Zn. In an investigation of multilength optical orthogonal codes (MLOOCs) of weight four, pairwise 2-compatible CRDFs with block size four play an important role. In this paper, we obtain some infinite classes of kk pairwise 2-compatible CRDFs with block size four by using cyclotomic classes and disjoint skew starters. Consequently, some infinite classes of optimal MLOOCs of weight four are obtained.