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We extend results of K. Lee and M.E. OʼSullivan by showing how to use Grobner 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.

Let F"q denote the finite field with q elements. The symmetric group S"n acts on the set G"n","q of all linear subspaces of F"q^n by permuting coordinates. We show that the normalized character of the associated permutation representation of S"n approaches the trivial character as n approaches infinity. We also consider the case of the wreath product of F"q^x and S"n acting on G"n","q, and formulate a conjecture that would yield the asymptotic number of distinct equivalence classes of q-ary linear codes.