Generalization of the Lee-O'Sullivan list decoding for one-point AG codes

摘要

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan (2009) based on Groebner 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 Groebner basis of a module proposed by Lee and O'Sullivan (2009), which was not possible in another generalization by Lax (2012).