Among the mesh compression algorithms, different schemes compress better specific categories of model. In particular, geometry-driven approaches have shown outstanding performances on isosurfaces. It would be expected these algorithm to also encode well meshes reconstructed from the geometry, or optimized by a geometric re-meshing. GEncode is a new single-rate compression scheme that compresses the connectivity of these meshes at almost zero-cost. It improves existing geometry-driven schemes for general meshes on both geometry and connectivity compression. This scheme extends naturally to meshes of arbitrary dimensions in arbitrary ambient space, and deals gracefully with non-manifold meshes. Compression results for surfaces are competitive with existing schemes.