Codes from the Suzuki function field

We construct algebraic geometry (AG) codes from the function field F(2²ⁿ⁺¹)(x,y)/F(2²ⁿ⁺¹) defined by y(2²ⁿ⁺¹)-y=(x(2²ⁿ⁺)-x) where n is a positive integer. These codes are supported by two places, and many have parameters that are better than those of any comparable code supported by one place of the same function field. To define such codes, we determine and exploit the structure of the Weierstrass gap set of an arbitrary pair of rational places of F(2²ⁿ⁺¹)(x,y)/F(2²ⁿ⁺¹). Moreover, we find some codes over F₈ with parameters that are better than any known code.