  The quantum group $SU_q(\ell+1)$ has a canonical action on the odd
dimensional sphere $S_q^{2\ell+1}$. All odd spectral triples acting on the
$L_2$ space of $S_q^{2\ell+1}$ and equivariant under this action have been
characterized. This characterization then leads to the construction of an
optimum family of equivariant spectral triples having nontrivial $K$-homology
class. These generalize the results of Chakraborty & Pal for $SU_q(2)$.
