Partial geometric codes
Oliver Pretzel · IEEE Transactions on Information Theory · 1999
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.