Finding a Basis of a Linear System with Pairwise Distinct Discrete Valuations on an Algebraic curve

摘要

Under the assumption that we have defining equations of an affine algebraic cuve in special position with respect to a rational place Q, we propose an algorithm computing a basis of L(D) of a divisor D from an ideal basis of the ideal L(D+∞Q) of the affine coordinate ring L(∞Q) of the given algebraic curve, where L(D+∞Q): =U~∞_i=1 L(D+ iQ). Elements in the basis produced by our algorithm have pairwise distinct discrete valuations at Q, which is convenient in the construction of algebraic geometry codes.