2012/08/09 by Qi Wang, Yue Zhou, Wang, Qi +1
Computer Science · Engineering · Mathematics · #05B10 #94A55 #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #G.2.1 #Information Theory (cs.IT) #acm:05B10 #acm:94A55 #cs.IT #graph theory and CDMA systems #math.CO #math.IT #msc:05B10 #msc:94A55
paper · pdf · doi:10.48550/arxiv.1208.1878
20 pages
openalex publication_date 2012/08/09 · arxiv created 2013/10/27 · arxiv updated 2013/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Zero-difference balanced (ZDB) functions can be employed in many applications, e.g., optimal constant composition codes, optimal and perfect difference systems of sets, optimal frequency hopping sequences, etc. In this paper, two results are summarized to characterize ZDB functions, among which a lower bound is used to achieve optimality in applications and determine the size of preimage sets of ZDB functions. As the main contribution, a generic construction of ZDB functions is presented, and many new classes of ZDB functions can be generated. This construction is then extended to construct a set of ZDB functions, in which any two ZDB functions are related uniformly. Furthermore, some applications of such sets of ZDB functions are also introduced.