  This paper is concerned with the construction of algebraic geometric codes
defined from Kummer extensions. It plays a significant role in the study of
such codes to describe bases for the Riemann-Roch spaces associated with
totally ramified places. Along this line, we give an explicit characterization
of Weierstrass semigroups and pure gaps. Additionally, we determine the floor
of a certain type of divisor introduced by Maharaj, Matthews and Pirsic.
Finally, we apply these results to find multi-point codes with good parameters.
As one of the examples, a presented code with parameters $ [254,228,\geqslant
16] $ over $ \mathbb{F}_{64} $ yields a new record.
