Some series of optimal multilength OOCs of weight four.

Two cyclic relative difference families ( n , g , w , 1 ) -CRDFs A and B are called 2-compatible if | ( A + x ) ∩ ( B + y ) | ≤ 2 for any A ∈ A , B ∈ B and x , y ∈ Z n . 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 k 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. [ABSTRACT FROM AUTHOR]