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