Non-geometric cospectral mates of line graphs with a linear representation

For an incidence geometry $${\mathcal G}= ({\mathcal P}, {\mathcal L}, {\text {I}})$$ with a linear representation T}_2^*({\mathcal K})$$ , we apply WQH switching to construct non-geometric graph $$\Gamma '$$ cospectral the line $$ of G}$$ . As application, show that for $$h \ge 2$$ and $$0< m < h$$ there are strongly regular graphs parameters $$(v, k, \lambda \mu ) = (2^{2\,h} (2^{m+h}+2^m-2^h), 2^h (2^h+1)(2^m-1), (2^{m+1}-3), (2^m-1))$$ which not point partial geometries order $$(s,t,\alpha ((2^h+1)(2^m-1), 2^h-1, 2^m-1)$$