“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 2311 |
|
||||
| Abstract: | |||||
|
A Hadamard matrix H of order 4n2 is called regular if every
row and column sum of H is 2n. A Bush-type Hadamard matrix is
a regular Hadamard matrix of order 4n2 with the additional
property of being a block matrix H=[Hij] with blocks of size
2n such that Hii=J2n and HijJ2n=J2nHij=0,i ≠ j, where Jm denotes the all-one m by m matrix.
A balanced generalized weighing matrix BGW(v,k,λ)
over a multiplicative group G is a v by v matrix
W=[gij] with entries from ―G=G∪{0} such that
each row of W contains exactly k nonzero entries, and for
every a, b ∈ { 1,..., v}, a ≠ b, the multi-set
{gaigbi−1 | 1 ≤ i ≤ v,gai ≠ 0,gbi ≠ 0}
contains exactly λ/|G|/ copies of each element of G.
In this paper a 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 (936,375,150,150) 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 twin strongly regular graph with
parameters (1800,1029,588,588) whose points can be partitioned in
50 cocliques of size 36.
Download TeX format |
|||||
| back to top | |||||
