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TitleGeneric interpolation polynomial for list decoding
Author(s) Robert F. Lax
TypeArticle in Journal
AbstractWe 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 one-point 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 1-error correcting codes for which a single error can be decoded by a very simple process involving substituting into the generic interpolation polynomial.
KeywordsList decoding, Interpolation polynomial, One-point AG code, Gröbner basis, Affine variety code
URL http://www.sciencedirect.com/science/article/pii/S1071579711000621
JournalFinite Fields and Their Applications
Pages167 - 178
Translation No
Refereed No