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August  2016, 10(3): 547-554. doi: 10.3934/amc.2016025

On the existence of Hadamard difference sets in groups of order 400

Joško Mandić 1, and  Tanja Vučičić 1,

1. 

Faculty of Science, University of Split, Rudjera Boškovića 33, Split, 21000, Croatia, Croatia

Received  May 2015 Revised  June 2016 Published  August 2016

This paper concerns the problem of the existence of Hadamard difference sets in nonabelian groups of order 400. By introducing a new construction method, we construct new difference sets in 20 groups. We survey non-existence results, verifying non-existence in 45 groups.
Keywords: difference set., Transitive incidence structure, block design.
Mathematics Subject Classification: Primary: 05B05, 05B1.
Citation: Joško Mandić, Tanja Vučičić. On the existence of Hadamard difference sets in groups of order 400. Advances in Mathematics of Communications, 2016, 10 (3) : 547-554. doi: 10.3934/amc.2016025
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show all references

References:
[1]

J. Combin. Des., 8 (2000), 221-231. doi: 10.1002/1520-6610(2000)8:4<221::AID-JCD1>3.3.CO;2-Y.  Google Scholar

[2]

Cambridge Univ. Press, 1999.  Google Scholar

[3]

edition 2.16, 2010. Google Scholar

[4]

Discrete Math., 118 (1993), 33-43. doi: 10.1016/0012-365X(93)90051-T.  Google Scholar

[5]

in Groups, Difference Sets and the Monster (eds. K.T. Arasu et al.), de Gruyter, Berlin-New York, 1996, 145-156.  Google Scholar

[6]

J. Combin. Theory Ser. A, 40 (1985), 9-21. doi: 10.1016/0097-3165(85)90043-3.  Google Scholar

[7]

Crypt. Commun., {2} (2010), 271-292. doi: 10.1007/s12095-010-0031-1.  Google Scholar

[8]

The GAP Group, GAP - Groups, Algorithms, and Programming, version 4.4,, available online at , ().   Google Scholar

[9]

J. Combin. Des., 9 (2001), 424-434. doi: 10.1002/jcd.1021.  Google Scholar

[10]

AMS, Providence, 2013. doi: 10.1090/stml/067.  Google Scholar

[11]

J. Combin. Theory Ser. A, 70 (1995), 144-156. doi: 10.1016/0097-3165(95)90084-5.  Google Scholar

[12]

J. Combin. Des., 8 (2000), 291-299. doi: 10.1002/1520-6610(2000)8:4<291::AID-JCD6>3.0.CO;2-L.  Google Scholar

[13]

=, ().   Google Scholar

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