  A toric quantum error-correcting code construction procedure is presented in
this work. A new class of an infinite family of toric quantum codes is provided
by constructing a classical cyclic code on the square lattice
$\mathbb{Z}_{q}\times \mathbb{Z}_{q}$ for all odd integers $q\geq 5$ and,
consequently, new toric quantum codes are constructed on such square lattices
regardless of whether $q$ can be represented as a sum of two squares.
Furthermore this work supplies for each $q$ the polyomino shapes that
tessellate the corresponding square lattices and, consequently, tile the
lattice $\mathbb{Z}^{2}$. The channel without memory to be considered for these
constructed toric quantum codes is symmetric, since the
$\mathbb{Z}^{2}$-lattice is autodual. Moreover, we propose a quantum
interleaving technique by using the constructed toric quantum codes which shows
that the code rate and the coding gain of the interleaved toric quantum codes
are better than the code rate and the coding gain of Kitaev's toric quantum
codes for $q=2n+1$, where $n\geq 2$, and of an infinite class of Bombin and
Martin-Delgado's toric quantum codes. In addition to the proposed quantum
interleaving technique improves such parameters, it can be used for burst-error
correction in errors which are located, quantum data stored and quantum
channels with memory.
