Since p, q, and d are variants, and all others are invariants (at least during construction) you'll want to offer the user the chance to set the variants in the constructor.
something like this:
LFSR::LFSR(int p_, int q_, int _d)
: p(p_)
, q(q_)
, d(d_)
{
}
Setting the invariants in the class definition as you have done will work with c++11, not with c++98.
If you have an older compiler you'll need to do this:
LFSR::LFSR(int p_, int q_, int d_)
: y(0)
, turnCount(0)
// ... all other member variables in order of definition ...
, p(p_)
, q(q_)
, d(d_)
, n(0)
// ... all the rest here ...
{
}