On the qth power algorithm

Leonard and Pellikaan developed the qth power algorithm to compute module bases for the integral closure of the polynomial ring Fq[x] in a class of function fields. In this paper, their algorithm is adapted to efficiently obtain an Fq-basis for a class of Riemann–Roch spaces without having to compute the entire integral closure. This reformulation allows one to determine the complexity of the algorithm. Further, we obtain a simple characterization of the integral closure.