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

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, λ=μ=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, λ=μ=588.