  Let $(R,{}^-)$ be an arbitrary unital associative superalgebra with
superinvolution over a commutative ring $\Bbbk$ with $2$ invertible. The second
homology of the generalized periplectic Lie superalgebra
$\mathfrak{p}_m(R,{}^-)$ for $m\geqslant3$ has been completely determined via
an explicit construction of its universal central extension. In particular,
this second homology could be identified with the first
$\mathbb{Z}/2\mathbb{Z}$-graded dihedral homology of $R$ with certain
superinvolution whenever $m\geqslant 5$.
