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http://dx.doi.org/10.4134/CKMS.2016.31.1.041

ON GENERALIZED ZERO-DIFFERENCE BALANCED FUNCTIONS  

Jiang, Lin (Institute of Mathematics and Software Science Sichuan Normal University)
Liao, Qunying (Institute of Mathematics and Software Science Sichuan Normal University)
Publication Information
Communications of the Korean Mathematical Society / v.31, no.1, 2016 , pp. 41-52 More about this Journal
Abstract
In the present paper, by generalizing the definition of the zero-difference balanced (ZDB) function to be the G-ZDB function, several classes of G-ZDB functions are constructed based on properties of cyclotomic numbers. Furthermore, some special constant composition codes are obtained directly from G-ZDB functions.
Keywords
zero-difference balanced (ZDB) function; generalized ZDB function; cyclotomic coset; difference system of sets; constant composition code;
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1 X. Zeng, H. Guo, and J. Yuan, A note of perfect nonlinear functions, in Cryptography and Network Security, vol. 4301 of Lecture Notes in Comput. Sci., 259-269, Berlin: Springer, 2006.
2 Z. Zha, G. M. Kyureghyan, and X. Wang, Perfect nonlinear binomials and their semifields, Finite Fields Appl. 15 (2009), no. 2, 125-133.   DOI
3 Z. Zhou, X. Tang, D. Wu, and Y. Yang, Some new classes of zero-difference balanced functions, IEEE Trans. Inform. Theory 58 (2012), no. 1, 139-145.   DOI
4 H. Cai, X. Zeng, T. Helleseth, X. Tang, and Y. Yang, A new construction of zero-difference balanced functions and its applications, IEEE Trans. Inform. Theory 59 (2013), no. 8, 5008-5015.   DOI
5 C. Ding, Optimal constant composition codes from zero-difference balanced functions, IEEE Trans. Inform. Theory 54 (2008), no. 12, 5766-5770.   DOI
6 C. Ding, Optimal and perfect difference systems of sets, J. Combin. Theory Ser. A 116 (2009), no. 1, 109-119.   DOI
7 T. Feng, A new construction of perfect nonlinear functions using Galois rings, J. Combin. Des. 17 (2009), no. 3, 229-239.   DOI
8 C. Ding and Y. Tan, Zero-difference balanced functions with applications, J. Stat. Theory Pract. 6 (2012), no. 1, 3-19.   DOI
9 C. Ding, Q. Wang, and M. S. Xiong, Three new families of zero-difference balanced functions with applications, arXiv preprint arXiv:1312.4252, 2013.
10 C. Ding and J. Yin, Combinatorial constructions of optimal constant-composition codes, IEEE Trans. Inform. Theory 51 (2005), no. 10, 3671-3674.   DOI
11 X. D. Hou, Cubic bent functions, Discrete Math. 189 (1998), no. 1-3, 149-161.   DOI
12 V. I. Levenstein, A certain method of constructing quasilinear codes that guarantee synchronization in the presence of errors, Problemy Peredaci Informacii 7 (1971), no. 3, 30-40.
13 V. I. Levenstein, Combinatorial problems motivated by comma-free codes, J. Combin. Des. 12 (2004), no. 3, 184-196.   DOI
14 Y. Luo, F. W. Fu, A. J. H. Vinck, and W. Chen, On constant-composition codes over ${\mathbb{Z}}_q$, IEEE Trans. Inform. Theory 49 (2003), no. 11, 3010-3016.   DOI
15 K. Nyberg, Perfect nonlinear S-boxes, in Advances in cryptology-EUROCRYPT'91 (Brighton, 1991), vol. 547 of Lecture Notes in Comput. Sci., 378-386, Berlin: Springer, 1991.
16 A. Pott and Q. Wang, Difference balanced functions and their generalized difference sets, arXiv preprint arXiv:1309.7842, 2013.
17 H. Wang, A new bound for difference systems of sets, J. Combin. Math. Combin. Comput. 58 (2006), 161-167.
18 S. Yan, Elementary Number Theory, Springer Berlin Heidelberg, 2002.