Ternary codes from the strongly regular (45, 12, 3, 3) graphs and orbit matrices of 2-(45, 12, 3) designs
نویسندگان
چکیده
منابع مشابه
The Strongly Regular (45, 12, 3, 3) Graphs
Using two backtrack algorithms based on different techniques, designed and implemented independently, we were able to determine up to isomorphism all strongly regular graphs with parameters v = 45, k = 12, λ = μ = 3. It turns out that there are 78 such graphs, having automorphism groups with sizes ranging from 1 to 51840.
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We show that there are exactly 4285 symmetric (45,12,3) designs that admit nontrivial automorphisms. Among them there are 1161 self-dual designs and 1562 pairs of mutually dual designs. We describe the full automorphism groups of these designs and analyze their ternary codes. R. Mathon and E. Spence have constructed 1136 symmetric (45,12,3) designs with trivial automorphism group, which means t...
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A backtrack search with isomorph rejection is carried out to enumerate the 2-(12,3,2) designs. There are 242 995 846 such designs, which have automorphism groups whose size range from 1 to 1536. There are 88 616 310 simple designs. The number of resolvable designs is 62 929; these have 74 700 nonisomorphic resolutions. We use the following standard notations. A t-(v, k, >.) design is a family o...
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AKI YAMADA,1 SUSUMU OHYA,2 MASARU HIRANO,2 MINORU WATANABE,2 MICHAEL P. WALSH,3 AND YUJI IMAIZUMI1 1Department of Pharmacology and Therapeutics and 2Department of Chemical Pharmacology, Faculty of Pharmaceutical Sciences, Nagoya City University, Nagoya 467-8603, Japan; and 3Department of Biochemistry and Molecular Biology, Faculty of Medicine, University of Calgary, Calgary, Alberta T2N 4N1, Ca...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.06.012