The weights of Hadamard matrices

Let $\text{Ω}{}_{\mathrm{n}}$ denote the set of all n × n Hadamard matrices. For $\text{H ∈ Ω}{}_{\mathrm{n}}$, define the weight of H to be w(H) = number of 1's in H, and $\text{w(n) =}\text{max}\text{{w(H); H ∈ Ω}{}_{\mathrm{n}}\text{}}$. In this paper, we derive upper and lower bounds for w(n).