Difference Systems of Sets with Nonzero Rate from Partitioned Difference Families

Abstract

Sequences and combinatorics, particularly in coding theory, have seen increasing attention in recent years, especially in the study of difference systems of sets (DSSs) and partitioned difference families (PDFs) also known as zero-difference balanced (ZDB) functions. This paper has two main objectives: first, to propose a new, generic construction method for optimal DSSs using PDFs, and second, to introduce a direct method for constructing PDFs over cyclic groups. This direct construction, combined with a recursive approach, can produce desirable PDFs that may be used to generate DSSs leading comma-free codes with relatively high code rates. Some of the DSSs produced through this new construction are optimal when compared to known theoretical bounds.