Three New Families of Zero-difference Balanced Functions with Applications

2013/12/16 by Cunsheng Ding, Qi Wang, Ding, Cunsheng +3
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Coding theory and cryptography #cs.IT #graph theory and CDMA systems #math.IT #msc:05B10 #msc:11T71

paper · pdf · doi:10.48550/arxiv.1312.4252

10 pages

arxiv created 2013/12/16 · arxiv updated 2013/12/17

Abstract

Zero-difference balanced (ZDB) functions integrate a number of subjects in combinatorics and algebra, and have many applications in coding theory, cryptography and communications engineering. In this paper, three new families of ZDB functions are presented. The first construction, inspired by the recent work \citeCai13, gives ZDB functions defined on the abelian groups (\gf(q₁) × ⋯ × \gf(q_k), +) with new and flexible parameters. The other two constructions are based on 2-cyclotomic cosets and yield ZDB functions on \Z_n with new parameters. The parameters of optimal constant composition codes, optimal and perfect difference systems of sets obtained from these new families of ZDB functions are also summarized.

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