Generalization of the Lee–OʼSullivan list decoding for one-point AG codes

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and OʼSullivan (2009), based on Gröbner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander (2010), . Our generalization enables us to apply the fast algorithm to compute a Gröbner basis of a module proposed by Lee and OʼSullivan (2009), , which was not possible in another generalization by Lax (2012).