). \end{aligned}$$ ]{} Consider another other pair $ \lbrace (\hat{s}_1,\hat{s}_2), (\hat{s}'_1,\hat{s}'_2)\rbrace \in \mathcal{S}^2_{\text{eff}} $ with $ \hat{s}_1,\, \hat{s}'_1,\,\hat{s}_2,\,\hat{s}'_2 \in \mathcal{S}$, and let $ \vert \triangle \hat{s}_j \vert =  \vert \hat{s}_j - \hat{s}'_j \vert $ and $ \hat{\phi}_j = \angle (\hat{s}_j-\hat{s}'_j) $ for $ j=1,\,2 $. If $ \vert \triangle \hat{s}_1 \vert = \vert \triangle s_1 \vert $, $ \vert \triangle \hat{s}_2 \vert = \vert \triangle  s_2 \vert $ and $ \hat{\phi}_2-\hat{\phi}_1 = \phi_2 - \phi_1 $ or $ \hat{\phi}_2-\hat{\phi}_1 = \pi -(\phi_2 - \phi_1) $, then from , $ d^2_{(\hat{s}_1,\hat{s}_2)\leftrightarrow (\hat{s}'_1,\hat{s}'_2)} = d^2_{(s_1,s_2)\leftrightarrow (s'_1,s'_2)} $ for all values of $ (\gamma, \theta) $, even though the value of this distance changes with $ (\gamma, \theta) $.

\[def:distclass\] A distance class denoted by $ \mathcal{C} $, is a subset of $ \mathcal{S}_{\text{eff}}^2 $, which contains the pairs of the form $ \lbrace (s_1,s_2),(s'_1,s'_2)\rbrace $, $ (s_1,s_2)\neq (s'_1,s'_2) $ where $ (s_1,s_2)$ and $(s'_1,s'_2) $ denote the complex points in $ \mathcal{S}_{eff} $, such that the distance between the two elements of a pair is same for all pairs in $ \mathcal{C} $ and this property holds for all values of $ \gamma $ and $ \theta $, though the value of 