Further improvements on the designed minimum distance of algebraic geometry codes

In the literature about algebraic geometry codes one finds a lot of results improving Goppa’s minimum distance bound. These improvements often use the idea of “shrinking” or “growing” the defining divisors of the codes under certain technical conditions. The main contribution of this article is to show that most of these improvements can be obtained in a unified way from one (rather simple) theorem. Our result does not only simplify previous results but it also improves them further.