List decoding codes on Garcia-Stictenoth tower using Gröbner basis

Authors:
M. Prem Laxman Das;Kripasindhu Sikdar
Affiliations:
The Institute of Mathematical Sciences, CIT Campus Taramani, 600 113 Chennai, Tamil Nadu, India;-
Venue:
Journal of Symbolic Computation
Year:
2009

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Abstract

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 Grobner 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.