Orbit-disjoint regular (n,3,1)(n,3,1)-CDPs and their applications to multilength OOCs

Two g  -regular cyclic difference packings of parameters (v,3,1)(v,3,1) (also termed as cyclically relative difference families (v,g,3,1)(v,g,3,1)-CRDFs) AA and BB are called orbit-disjoint if {A+x:A∈A,x∈Zv}∩{B+x:B∈B,x∈Zv}=∅. In an investigation of multilength optical orthogonal codes (MLOOCs) with weight three, pairwise orbit-disjoint g  -regular cyclic difference packings with block size three play an important role. In this paper, we use cyclotomic classes to obtain some pairwise orbit-disjoint (v,g,3,1)(v,g,3,1)-CRDFs. Consequently, some infinite classes of optimal MLOOCs with weight three are obtained.