Abstract
We use Weierstrass gaps of points (places) to improve the lower bounds on the minimum distance and covering radius of Goppa codes and Reed-Solomon (RS) codes from function fields over finite fields. As a consequence, we show the existence of many optimal and sub-optimal codes from algebraic geometry. We give necessary conditions for equality to hold in the lower bound on the minimum distance of Goppa codes. An upper bound on the minimum distance of some RS codes (Goppa codes) is also derived.
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