A binary linear code of length and rank is a -dimensional vector subspace . Its minimum distance is the least Hamming weight of a nonzero codeword, equivalently the least Hamming distance between distinct codewords.
Write
and assume so that is identifiable.
The group
acts on the Poincaré half-plane model by
A direct calculation gives
Therefore
so every element of PSL2(R) is an isometry of the hyperbolic metric.

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