The Constructions Of Partitioned Difference Families

Partitioned difference families(PDFs) were put forward by C. Ding and J. Yin indealing with the construction of constant composition codes(CCCs). Constant compo-sition codes(CCCs) are a special class of constant weight codes, they were introducedin powerline communication and balanced scheduling. It is widely used in the design ofoligonucleotide sequences for DNA computing, the coding for bandwidth-effcient chan-nels and the construction of spherical codes for modulation etc.. In dealing with the codesynchronization problem, the difference system of sets(DSSs) are commonly used. Thedifference system of sets was introduced by Levenshtein in 2004. Besides, partitioneddifference families are related to zero-di?erence balanced functions which can constructconstant composition codes and difference system of sets.Yin and Wang et al. constructed some partitioned difference families using cyclo-tomic difference sets, Wang chengmin et al. got some partitioned difference families by1-rotational resolvable balanced incomplete block design. However, the results of parti-tioned difference families is rare because of its rigorous conditions.In this paper, we get several partitioned difference families by splitting and integrat-ing cyclotomies of field. At the same time, we obtain a few of almost difference familiesand disjoint difference families.