Multi-point Codes from the GGS Curves

This paper is concerned with the construction of algebraic geometric codes defined from GGS curves. It is of significant use to describe bases for the Riemann-Roch spaces associated to some totally ramified places, which enables us to study multi-point AG codes. Along this line, we characterize explicitly the Weierstrass semigroups and pure gaps by an exhaustive computation of the basis for Riemann-Roch spaces from GGS curves. Additionally, we determine the floor of a certain type of divisor and investigate the properties of AG codes. Finally, we apply these results to find multi-point codes with excellent parameters. As one of the examples, a presented code with parameters [216, 190,> 18] over F64 yields a new record.