  Gaberdiel and Gopakumar recently proposed that the tensionless limit of
string theory on $AdS_3 \times S^3 \times T^4$ takes the form of a higher spin
theory with a gauge algebra that is referred to as the higher spin square. In
this note, we formulate the linearized Vasiliev-type equations which describe a
matter field coupled to the higher spin square. We study the particle spectrum
of this field and show that it accounts for the entire untwisted sector of the
dual symmetric orbifold CFT, thereby confirming a conjecture by Gaberdiel and
Gopakumar. In doing so, we pinpoint the group-theoretic data which determine
the spectrum of a matter field coupled to a general higher spin algebra, which
we illustrate by revisiting the theory based on the $hs[1/2]$ algebra.
