Sets of zero-difference balanced functions and their applications

Qi Wang; Yue Zhou

doi:10.3934/amc.2014.8.83

Article Contents

2014, Volume 8, Issue 1: 83-101. Doi: 10.3934/amc.2014.8.83

This issue Previous Article Self-dual [62, 31, 12] and [64, 32, 12] codes with an automorphism of order 7 Next Article Heuristics of the Cocks-Pinch method

Sets of zero-difference balanced functions and their applications

Qi Wang^1, and
Yue Zhou^2,

1.
Institute of Algebra and Geometry, Otto-von-Guericke University Magdeburg, 39106 Magdeburg
2.
Department of Mathematics and System Sciences, National University of Defense Technology, Changsha, Hunan 410073

Received: March 2013

Revised: September 2013

Published: February 2014

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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.

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Mathematics Subject Classification: Primary: 05B10; Secondary: 94A55.

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