Abstract
In this article we provide a complete classification of regular partial difference sets in Abelian groups of order \(4p^2\), p an odd prime. It turns out that the known examples are the only examples. These are, up to complements, the trivial examples, the PCP examples, and a sporadic example in \(\mathbb {Z}_2^2\times \mathbb {Z}_3^2\).
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References
Arasu K.T., Jungnickel D., Ma S.L., Pott A.: Strongly regular Cayley graphs with \(\lambda -\mu =-1\). J. Comb. Theory Ser. A 67, 116–125 (1994).
Beth T., Jungnickel D., Lenz H.: Design Theory, 2nd edn. Cambridge University Press, Cambridge (1999).
De Winter S., Kamischke E., Wang Z.: Automorphisms of strongly regular graphs with applications to partial difference sets. Des. Codes Cryptogr. 79, 471–485 (2016).
Jørgensen L.K., Klin M.: Switching of edges in strongly regular graphs. I. A family of partial difference sets on 100 vertices. Electron. J. Comb. 10, R17 (2003).
Ma S.L.: A survey of partial difference sets. Des. Codes Cryptogr. 4, 221–261 (1994).
Ma S.L.: Some necessary conditions on the parameters of partial difference sets. J. Stat. Plan. Inference 62, 47–56 (1997).
McFarland R.L.: Sub-difference sets of Hadamard difference sets. J. Comb. Theory Ser. A 54, 112–122 (1990).
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Communicated by D. Jungnickel.
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De Winter, S., Wang, Z. Classification of partial difference sets in Abelian groups of order \(4p^2\) . Des. Codes Cryptogr. 84, 451–461 (2017). https://doi.org/10.1007/s10623-016-0280-x
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DOI: https://doi.org/10.1007/s10623-016-0280-x
Keywords
- Partial difference set
- Local multiplier theorem
- Characteristic matrix
Mathematics Subject Classification
- 05E30
- 05B10
- 05C50