List decoding codes on Garcia-Stictenoth tower using Groebner basis

摘要

An account of the interpolation and the root-finding steps of list decoding of one-point codes is given. The interpolation step is reduced to the problem of finding the minimal element of the Groebner basis of a submodule of a free module over a polynomial ring of one variable. The procedure for root-finding of the interpolation polynomial going modulo a large degree place is described from the tower point of view.