Recoletos Multidisciplinary Research Journal

Articles

Vol. 10 No. 1 (2022)

Construction of Difference Sets from Unions of Cyclotomic Classes of Order N=14

DOI:
https://doi.org/10.32871/rmrj2210.01.04
Submitted
March 24, 2022
Published
May 29, 2022
FULL PAPER

Keywords

  • difference set
  • cyclotomic class
  • union
  • computer search

Abstract

abstract_CONSTRUCTIVE_OF_DIFFERENCE_SETS.PNG

References

  1. Balmaceda, J. M. P., & Estrella, B. M. (2021). Difference sets from unions of cyclotomic classes of orders 12, 20, and 24. Philippine Journal of Science, 150 (6B), 1803–1810.
  2. Baumert, L.D., & Fredricksen, H. (1967). The cyclotomic numbers of order eighteen with applications to difference sets. Mathematics of Computation, 21(98), 204-219. https://www.ams.org/journals/mcom/1967-21-098/S0025-5718-1967-0223322-5/S0025-5718-1967-0223322-5.pdf
  3. Beth, T., Jungnickel, D., & Lenz, H. (1999). Design theory (2nd ed., Vol. 1). Cambridge University Press.
  4. Ding, C. (2015). Codes from difference sets. World Scientific.
  5. Estrella, B. M. (2019). Generating difference sets from Unions of Cyclotomic classes [Unpublished master’s thesis]. University of the Philippines Diliman.
  6. Feng, T., Momihara, K., & Xiang, Q. (2015). Constructions of strongly regular Cayley graphs and skew Hadamard difference sets from cyclotomic classes. Combinatorica, 35(4), 413–434.
  7. Feng, T., & Xiang, Q. (2012). Cyclotomic constructions of Skew Hadamard difference sets. Journal of Combinatorial Theory, Series A, 119(1), 245–256. https://doi.org/10.1016/j.jcta.2011.08.007
  8. Hall, M. (1956). A survey of difference sets. Proceedings of the American Mathematical Society, 7(6), 975-986.
  9. Hayashi, H. S. (1965). Computer investigation of difference sets. Mathematics of Computation, 19(89), 73–78. https://doi.org/10.1090/s0025-5718-1965-0171368-6
  10. Momihara, K. (2013). Inequivalence of Skew Hadamard difference sets and triple intersection numbers modulo a prime. The Electronic Journal of Combinatorics, 20(4). https://doi.org/10.37236/3762
  11. Momihara, K., Wang, Q., & Xiang, Q. (2019). 9. Cyclotomy, difference sets, sequences with low correlation, strongly regular graphs and related geometric substructures. In K.-U. Schmidt & A. Winterhof (Eds.), Combinatorics and finite fields: Difference sets, polynomials, pseudorandomness and applications (pp. 173–198). De Gruyter.
  12. Moore, E. H., & Pollatsek, H. S. (2013). Difference sets: Connecting algebra, combinatorics, and geometry (Vol. 67). American Mathematical Society.
  13. Xia, B. (2018). Cyclotomic difference sets in finite fields. Mathematics of Computation, 87(313), 2461–2482. https://doi.org/10.1090/mcom/3311

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