On the qth power algorithm

Authors:
Xiaochun Hu;Hiren Maharaj
Affiliations:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA;Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA
Venue:
Finite Fields and Their Applications
Year:
2008

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Abstract

Leonard and Pellikaan developed the qth power algorithm to compute module bases for the integral closure of the polynomial ring F"q[x] in a class of function fields. In this paper, their algorithm is adapted to efficiently obtain an F"q-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.