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https://doi.org/10.21857/ypn4oc88w9

Hadamard difference sets and related combinatorial objects in groups of order 144

Tanja Vučičić   ORCID icon orcid.org/0000-0003-1574-6297 ; Faculty of Science, University of Split, Ruđera Boškovića 33, 21 000 Split, Croatia

Puni tekst: engleski, pdf (222 KB) str. 13-29 preuzimanja: 327* citiraj
APA 6th Edition
Vučičić, T. (2019). Hadamard difference sets and related combinatorial objects in groups of order 144. Rad Hrvatske akademije znanosti i umjetnosti, (538=23), 13-29. https://doi.org/10.21857/ypn4oc88w9
MLA 8th Edition
Vučičić, Tanja. "Hadamard difference sets and related combinatorial objects in groups of order 144." Rad Hrvatske akademije znanosti i umjetnosti, vol. , br. 538=23, 2019, str. 13-29. https://doi.org/10.21857/ypn4oc88w9. Citirano 29.09.2021.
Chicago 17th Edition
Vučičić, Tanja. "Hadamard difference sets and related combinatorial objects in groups of order 144." Rad Hrvatske akademije znanosti i umjetnosti , br. 538=23 (2019): 13-29. https://doi.org/10.21857/ypn4oc88w9
Harvard
Vučičić, T. (2019). 'Hadamard difference sets and related combinatorial objects in groups of order 144', Rad Hrvatske akademije znanosti i umjetnosti, (538=23), str. 13-29. https://doi.org/10.21857/ypn4oc88w9
Vancouver
Vučičić T. Hadamard difference sets and related combinatorial objects in groups of order 144. Rad Hrvatske akademije znanosti i umjetnosti [Internet]. 2019 [pristupljeno 29.09.2021.];(538=23):13-29. https://doi.org/10.21857/ypn4oc88w9
IEEE
T. Vučičić, "Hadamard difference sets and related combinatorial objects in groups of order 144", Rad Hrvatske akademije znanosti i umjetnosti, vol., br. 538=23, str. 13-29, 2019. [Online]. https://doi.org/10.21857/ypn4oc88w9

Sažetak
In this paper we address an appealing and so far not completed combinatorial problem of difference set (DS) existence in groups of order 144. We apply our recently established method for DS construction which proves to be very efficient. The result is more than 5000 inequivalent (144, 66, 30) DSes obtained in 131 groups of order 144. The number of nonisomorphic symmetric designs rising from them is 1364.

Using the obtained DSes as a source, new regular (144, 66, 30, 30) and (144, 65, 28, 30) partial difference sets are constructed, together with the corresponding strongly regular graphs. 43 non-isomorphic graphs of valency 66 are obtained and 78 of valency 65. The full automorphism groups of these graphs, as well as those of symmetric designs, are explored using the software package Magma.

Ključne riječi
Transitive incidence structure; (partial) difference set; strongly regular graph.

Hrčak ID: 225227

URI
https://hrcak.srce.hr/225227

Posjeta: 502 *