We present a theory of partial geometric Goppa (1981) codes, which can be applied to curves for which the genus is not explicitly known. That is often the case if the curve is nonsmooth or nonplanar. The only algebraic geometry required is familiarity with the basic concepts. Yet we are able to give a full account of all one-point codes including their error processors. We are also able to give a completely explicit construction for the initial code in a good sequence of codes based on a set of curves introduced by Garcia and Stichtenoth (Acad. Sci., Paris, vol.322 I, p.1067-70, 1996), for which the genus has not been determined.

Those functions defined on the cycles of a finite graph G that can be the flow difference of an orientation of G are characterized. The result is applied to give a proof of Bandelt’s Theorem stating that all (Hasse-) diagram orientations of a planar graph G have zero flow difference on all cycles if and only if G has a cycle basis of 4-cycles.