Advances in Mathematics of Communications (AMC)

Sets of zero-difference balanced functions and their applications

Pages: 83 - 101, Volume 8, Issue 1, February 2014      doi:10.3934/amc.2014.8.83

       Abstract        References        Full Text (433.5K)       Related Articles       

Qi Wang - Institute of Algebra and Geometry, Otto-von-Guericke University Magdeburg, 39106 Magdeburg, Germany (email)
Yue Zhou - Department of Mathematics and System Sciences, National University of Defense Technology, Changsha, Hunan 410073, China (email)

Abstract: 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.

Keywords:  Constant weight code, set of frequency-hopping sequences, partitioned di erence family, zero-di erence balanced function.
Mathematics Subject Classification:  Primary: 05B10; Secondary: 94A55.

Received: March 2013;      Revised: September 2013;      Available Online: January 2014.