2018/11/20 by Zongxiang Yi, Yi, Zongxiang, Dingyi Pei +2 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #Cryptography and Security (cs.CR) #DNA and Biological Computing #FOS: Computer and information sciences #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1811.08132
openalex publication_date 2018/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A function f from an Abelian group (A,+) to an Abelian group (B,+) is (n, m, S) zero-difference (ZD), if S=\λα| α∈ A∖\0\\ where n=|A|, m=|f(A)| and λα=|\x ∈ A | f(x+α)=f(x)\|. A function is called zero-difference balanced (ZDB) if S=\λ\ where λ is a constant number. ZDB functions have many good applications. However it is point out that many known zero-difference balanced functions are already given in the language of partitioned difference family (PDF). The problem that whether zero-difference ``not balanced" functions still have good applications as ZDB functions, is investigated in this paper. By using the change point technic, zero-difference functions with good applications are constructed from known ZDB functions. Then optimal difference systems of sets (DSS) and optimal frequency-hopping sequences (FHS) are obtained with new parameters. Furthermore the sufficient and necessary conditions of these objects being optimal, are given.