  A recursive approach to determine the Hilbert-Schmidt measure of pairwise
quantum discord in a special class of symmetric states of $k$ qubits is
presented. We especially focus on the reduced states of $k$ qubits obtained
from a balanced superposition of symmetric $n$-qubit states (multiqubit
Schr\"odinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots
,n-1)$. Two pairing schemes are considered. In the first one, the geometric
discord measuring the correlation between one qubit and the party grouping
$(k-1)$ qubits is explicitly derived. This uses recursive relations between the
Fano-Bloch correlation matrices associated with subsystems comprising $k$,
$k-1$, $\cdots$ and $2$ particles. A detailed analysis is given for two, three
and four qubit systems. In the second scheme, the subsystem comprising the
$(k-1)$ qubits is mapped into a system of two logical qubits. We show that
these two bipartition schemes are equivalents in evaluating the pairwise
correlation in multi-qubits systems. The explicit expressions of classical
states presenting zero discord are derived.
