Have a personal or library account? Click to login
Balance and Pattern Distribution of Sequences Derived from Pseudorandom Subsets of ℤq Cover

Balance and Pattern Distribution of Sequences Derived from Pseudorandom Subsets of ℤq

Open Access
|Feb 2022

References

  1. ALLOUCHE, J.-P.—SHALLIT, J.: Automatic sequences. Theory, applications, generalizations. Cambridge University Press, Cambridge, 2003.<a href="https://doi.org/10.1017/CBO9780511546563" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1017/CBO9780511546563</a>
  2. CHEN, Z.: Large families of pseudo-random subsets formed by generalized cyclotomic classes, Monatsh. Math. 161 (2010), no. 2, 161–172.
  3. COBELI, C.—ZAHARESCU, A.: On the distribution of primitive roots mod p, Acta Arith. 83 (1998), no. 2, 143–153.
  4. DARTYGE, C.—MOSAKI, E.—SÁRKÖZY, A.: On large families of subsets of the set of the integers not exceeding N, Ramanujan J. 18 (2009), no. 2, 209–229.
  5. DARTYGE, C.—SÁRKÖZY, A.: On pseudo-random subsets of the set of the integers not exceeding N, Period. Math.Hungar. 54 (2007), no. 2, 183–200.
  6. DARTYGE, C.—SÁRKÖZY, A.: Large families of pseudorandom subsets formed by power residues, Unif. Distrib. Theory 2 (2007), no. 2, 73–88.
  7. DARTYGE, C.—SÁRKÖZY, A.: On pseudo-random subsets of ℤn, Monatsh. Math. 157 (2009), no. 1, 13–35.
  8. DARTYGE, C.—SÁRKÖZY, A.—SZALAY, M.: On the pseudo-randomness of subsets related to primitive roots, Combinatorica 30 (2010), no. 2, 139–162.
  9. DING, C.: Pattern distributions of Legendre sequences, IEEE Trans. Inform. Theory 44 (1998), no. 4, 1693–1698.
  10. GYARMATI, K.: On a family of pseudo-random binary sequences, Period. Math. Hungar. 49 (2004), no. 2, 45–63.
  11. HARDY, G. H.—WRIGHT, E. M.: An introduction to the theory of numbers. Fifth edition. The Clarendon Press, Oxford University Press, New York, 1979.
  12. LIU, H.—QI, Y.: On multi-dimensional pseudorandom subsets, J. Number Theory 181 (2017), 73–88.<a href="https://doi.org/10.1016/j.jnt.2017.05.025" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/j.jnt.2017.05.025</a>
  13. LIU, H.—SONG, E.: A note on pseudorandom subsets formed by generalized cyclotomic classes, Publ. Math. Debrecen 85 (2014), no. 3-4, 257–271.
  14. LIU, H.—ZHANG, G.: Pseudo-random subsets constructed by using Fermat quotients, Publ. Math. Debrecen 94 (2019), no. 1-2, 55–74.
  15. WINTERHOF, A.—XIAO, Z.: Binary sequences derived from differences of consecutive primitive roots, IEEE Trans. Inform.Theory 67 (2021), no. 8, 5334–5338.
  16. WINTERHOF, A.—XIAO, Z.: Binary sequences derived from differences of consecutive quadratic residues, Adv. Math. Commun. to be published, doi: <a href="https://doi.org/10.3934/amc.2020100.10.3934/amc.2020100" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.3934/amc.2020100.10.3934/amc.2020100</a>
DOI: https://doi.org/10.2478/udt-2021-0009 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Language: English
Page range: 89 - 108
Submitted on: Oct 15, 2021
Accepted on: Nov 9, 2021
Published on: Feb 2, 2022
Published by: Slovak Academy of Sciences
In partnership with: Paradigm Publishing Services
Publication frequency: 2 times per year

© 2022 Huaning Liu, Arne Winterhof, published by Slovak Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.