대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제31권1호
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  • Pages.41-52
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  • 2016
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2015.04.07
  • 발행 : 2016.01.31
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초록

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.

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참고문헌

  1. 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. https://doi.org/10.1109/TIT.2013.2255114
  2. C. Ding, Optimal constant composition codes from zero-difference balanced functions, IEEE Trans. Inform. Theory 54 (2008), no. 12, 5766-5770. https://doi.org/10.1109/TIT.2008.2006420
  3. C. Ding, Optimal and perfect difference systems of sets, J. Combin. Theory Ser. A 116 (2009), no. 1, 109-119. https://doi.org/10.1016/j.jcta.2008.05.007
  4. C. Ding and Y. Tan, Zero-difference balanced functions with applications, J. Stat. Theory Pract. 6 (2012), no. 1, 3-19. https://doi.org/10.1080/15598608.2012.647479
  5. C. Ding, Q. Wang, and M. S. Xiong, Three new families of zero-difference balanced functions with applications, arXiv preprint arXiv:1312.4252, 2013.
  6. C. Ding and J. Yin, Combinatorial constructions of optimal constant-composition codes, IEEE Trans. Inform. Theory 51 (2005), no. 10, 3671-3674. https://doi.org/10.1109/TIT.2005.855612
  7. T. Feng, A new construction of perfect nonlinear functions using Galois rings, J. Combin. Des. 17 (2009), no. 3, 229-239. https://doi.org/10.1002/jcd.20213
  8. X. D. Hou, Cubic bent functions, Discrete Math. 189 (1998), no. 1-3, 149-161. https://doi.org/10.1016/S0012-365X(98)00008-9
  9. 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.
  10. V. I. Levenstein, Combinatorial problems motivated by comma-free codes, J. Combin. Des. 12 (2004), no. 3, 184-196. https://doi.org/10.1002/jcd.10071
  11. 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. https://doi.org/10.1109/TIT.2003.819339
  12. 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.
  13. A. Pott and Q. Wang, Difference balanced functions and their generalized difference sets, arXiv preprint arXiv:1309.7842, 2013.
  14. H. Wang, A new bound for difference systems of sets, J. Combin. Math. Combin. Comput. 58 (2006), 161-167.
  15. S. Yan, Elementary Number Theory, Springer Berlin Heidelberg, 2002.
  16. 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.
  17. Z. Zha, G. M. Kyureghyan, and X. Wang, Perfect nonlinear binomials and their semifields, Finite Fields Appl. 15 (2009), no. 2, 125-133. https://doi.org/10.1016/j.ffa.2008.09.002
  18. 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. https://doi.org/10.1109/TIT.2011.2171418

피인용 문헌

  1. Some New Constructions for Generalized Zero-Difference Balanced Functions vol.27, pp.08, 2016, https://doi.org/10.1142/S0129054116500362
  2. New classes of generalized zero-difference balanced functions and their applications vol.42, pp.1, 2019, https://doi.org/10.1080/02533839.2018.1537805