  Tanner codes are long error correcting codes obtained from short codes and a
graph, with bits on the edges and parity-check constraints from the short codes
enforced at the vertices of the graph. Combining good short codes together with
a spectral expander graph yields the celebrated expander codes of Sipser and
Spielman, which are asymptotically good classical LDPC codes.
  In this work we apply this prescription to the left-right Cayley complex that
lies at the heart of the recent construction of a $c^3$ locally testable code
by Dinur et al. Specifically, we view this complex as two graphs that share the
same set of edges. By defining a Tanner code on each of those graphs we obtain
two classical codes that together define a quantum code. This construction can
be seen as a simplified variant of the Panteleev and Kalachev asymptotically
good quantum LDPC code, with improved estimates for its minimum distance. This
quantum code is closely related to the Dinur et al. code in more than one
sense: indeed, we prove a theorem that simultaneously gives a linearly growing
minimum distance for the quantum code and recovers the local testability of the
Dinur et al. code.
