  In 2019, Perondi and Carmelo determined the set multipartite Ramsey number of
particular complete bipartite graphs by establishing a relationship between the
set multipartite Ramsey number, Hadamard matrices, and strongly regular graphs,
which is a breakthrough in Ramsey theory. However, since Hadamard matrices of
order not divisible by 4 do not exist, many open problems have arisen.
  In this paper, we generalize Perondi and Carmelo's results by introducing the
$[\alpha]$-Hadamard matrix that we conjecture exists for arbitrary order.
Finally, we determine set and size multipartite Ramsey numbers for particular
complete bipartite graphs.
