Abstract
We investigate the existence of (v, k, λ)-difference sets in noncyclic Abelian groups for k≤100.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature Cited
M. Hall, Combinatorial Theory [Russian translation], Mir, Moscow (1970).
E. Berlekamp, Mathematical Coding Theory [Russian translation], Mir, Moscow (1971).
L. E. Kopilovich and L. G. Sodin, “Nonequidistant sparse antenna arrays with optimal location of radiating elements using difference sets,” Dokl. AN UkrSSR, Ser. A, No. 9, 45–48 (1986).
L. D. Baumert, Cyclic Difference Sets, Lect. Notes Math.,182, Springer, New York (1971).
R. E. Kibler, “A summary of noncylic difference sets, k<20,” J. Combin. Theory, ser. A,25, No. 1, 62–67 (1978).
E. S. Lander, Symmetric Designs: An Algebraic Approach, Math. Soc. Lect. Note Ser., No. 74, Cambridge Univ. Press (1983).
R. J. Turyn, “Character sums and difference sets,” Pac. J. Math.,15, No. 1, 319–346 (1965).
H. B. Mann, Difference sets in elementary Abelian groups,” Illinois J. Math.,9, No. 2, 212–219 (1965).
D. R. Hughes, “On biplanes and semibiplanes,” Lect. Notes Math.,686, 55–58 (1978).
L. D. Baumert, “Difference sets,” SIAM J. Appl. Math.,17, No. 4, 826–833 (1969).
H. B. Mann, Addition Theorems, Interscience Publ, New York (1970).
R. H. Bruck, “Difference sets in a finite group,” Trans. AMS,78, No. 2, 464–481 (1955).
R. L. McFarland, “A family of difference sets in noncyclic groups,” J. Combin. Theory, Ser. A,15, No. 1, 1–10 (1973).
J. F. Dillon, “Variations of a scheme of McFarland for noncylic difference sets,” J. Combin. Theory, Ser. A,40, No. 1, 9–21 (1985).
Additional information
Translated from Kibernetika, No. 2, pp. 20–23, March–April, 1989.
Rights and permissions
About this article
Cite this article
Kopilovich, L.E. Difference sets in noncyclic Abelian groups. Cybern Syst Anal 25, 153–157 (1989). https://doi.org/10.1007/BF01070123
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01070123