Details:
Title  Generic interpolation polynomial for list decoding  Author(s)  Robert F. Lax  Type  Article in Journal  Abstract  We extend results of K. Lee and M.E. OʼSullivan by showing how to use Gröbner bases to find the interpolation polynomial for list decoding a onepoint AG code C = C L ( r P , D ) on any curve X , where P is an F q rational point on X and D = P 1 + P 2 + ⋯ + P n is the sum of other F q rational points on X . We then define the generic interpolation polynomial for list decoding such a code. The generic interpolation polynomial should specialize to the interpolation polynomial for most received strings. We give an example of a family of Reed–Solomon 1error correcting codes for which a single error can be decoded by a very simple process involving substituting into the generic interpolation polynomial.  Keywords  List decoding, Interpolation polynomial, Onepoint AG code, Gröbner basis, Affine variety code  ISSN  10715797 
URL 
http://www.sciencedirect.com/science/article/pii/S1071579711000621 
Language  English  Journal  Finite Fields and Their Applications  Volume  18  Number  1  Pages  167  178  Year  2012  Edition  0  Translation 
No  Refereed 
No 
