On the Construction of Codes from an Asymptotically Good Tower over F8

In 2002, van der Geer and van der Vlugt gave explicit equations for an asymptotically good tower of curves over the field F8. In this paper, we will present a method for constructing Goppa codes from these curves as well as explicit constructions for the third level of the tower. The approach is to find an associated plane curve for each curve in the tower and then to use the algorithms of Haché and Le Brigand to find the corresponding Goppa codes.