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A Block Negacyclic Bush-Type Hadamard Matrix and Two Strongly Regular Graphs

✍ Scribed by Zvonimir Janko; Hadi Kharaghani

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 84 KB
Volume: 98
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2001.3231

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✦ Synopsis

A block negacyclic Bush-type Hadamard matrix of order 36 is used in a symmetric BGW (26, 25, 24) with zero diagonal over a cyclic group of order 12 to construct a twin strongly regular graph with parameters v=936, k=375, l=m=150 whose points can be partitioned in 26 cocliques of size 36. The same Hadamard matrix then is used in a symmetric BGW (50, 49, 48) with zero diagonal over a cyclic group of order 12 to construct a Siamese twin strongly regular graph with parameters v=1800, k=1029, l=m=588.

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✍ Zvonimir Janko 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 102 KB

A nonsymmetric Bush-type Hadamard matrix of order 36 is constructed which leads to two new infinite classes of symmetric designs with parameters: where m is any positive integer.