Michael H. Freedman and David A. Meyer,
``Projective plane and planar quantum codes'',
Foundations of Computational Mathematics 1 (2001) 325-332;
quant-ph/9810055.

Cellulations of the projective plane RP² define single qubit topological quantum error correcting codes since there is a unique essential cycle in H₁(RP² ; Z₂). We construct three of the smallest such codes, show they are inequivalent, and identify one of them as Shor's original 9 qubit repetition code. We observe that Shor's code can be constructed in a planar domain and generalize to planar constructions of higher genus codes for multiple qubits.

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