Generalized distance-squared mappings of ${\mathbb{R}}^{n+1}$ into ${\mathbb{R}}^{2n+1}$

We classify generalized distance-squared mappings of ${\mathbb{R}}^{n+1}$ into ${\mathbb{R}}^{2n+1}$ ($n\ge 1$) having generic central points. Moreover, we show that there does not exist a universal bad set $\Sigma\subset ($\mathbb{R}$^{n+1})^{2n+1}$ in the case of this dimension-pair.