Finding the defining functions for one-point algebraic-geometry codes

An iterative algorithm is given for producing the parity-check functions fo r one-point algebraic-geometry (AG) codes, in particular (but not limited t o) those related to the two towers of function fields introduced by Garcia and Stichtenoth. This simple method, based on the linearity of the Qth-powe r map over F-Q, is an alternative to the method of using Laurent series exp ansions. Examples are given for small values of m with characteristic p = 2 for both towers.