On Multipliers of Difference Sets

Robert McFarland; H. B. Mann

doi:10.4153/CJM-1965-054-3

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Multipliers are useful in constructing difference sets as well as in impossibility proofs. The existence of a fixed set facilitates their application, so that the results of this paper should prove to be useful in numerical work concerning difference sets.

Let G be a group which we shall write multiplicatively. For any set A of elements of G, we define

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Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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Ganley, Michael J 1977. Direct product difference sets. Journal of Combinatorial Theory, Series A, Vol. 23, Issue. 3, p. 321.

McFarland, Robert L. and Rice, Bart F. 1978. Translates and multipliers of abelian difference sets. Proceedings of the American Mathematical Society, Vol. 68, Issue. 3, p. 375.

Wu, Xiaohong 1986. Extraneous multipliers of cyclic difference sets. Journal of Combinatorial Theory, Series A, Vol. 42, Issue. 2, p. 259.

McFarland, Robert L. and Ma, Siu Lun 1990. Abelian difference sets with multiplier minus one. Archiv der Mathematik, Vol. 54, Issue. 6, p. 610.

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Ma, S. L. 1991. McFarland's conjecture on abelian difference sets with multiplier ?1. Designs, Codes and Cryptography, Vol. 1, Issue. 4, p. 321.

Schmidt, Bernhard 1998. Nonexistence of a (783,69,6)-difference set. Discrete Mathematics, Vol. 178, Issue. 1-3, p. 283.

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Leung, Ka Hin Ma, Siu Lun and Schmidt, Bernhard 2014. A multiplier theorem. Journal of Combinatorial Theory, Series A, Vol. 124, Issue. , p. 228.

Turner, Jonathan S. Bulutoglu, Dursun A. Baczkowski, Daniel and Geyer, Andrew J. 2022. Counting the decimation classes of binary vectors with relatively prime length and density. Journal of Algebraic Combinatorics, Vol. 55, Issue. 1, p. 61.

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On Multipliers of Difference Sets

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