WEIERSTRASS SEMIGROUP AND CODES OVER THE CURVE y~q + y = x~(q~r +1)

摘要

We compute the Weierstrass semigroup at a pair of rational points on the curve defined by the affine equation y~q + y = x~(q~r +1) over F_q~(2r), where r is a positive odd integer and q is a prime power. We then construct a two-point AG code on the curve whose relative parameters are better than comparable one-point AG code.