# American Institute of Mathematical Sciences

November  2010, 4(4): 485-518. doi: 10.3934/amc.2010.4.485

## Efficient list decoding of a class of algebraic-geometry codes

 1 DTU-Mathematics, Technical University of Denmark, Matematiktorvet 303S, 2800 Kgs. Lyngby, Denmark, Denmark

Received  November 2009 Revised  May 2010 Published  November 2010

We consider the problem of list decoding algebraic-geometry codes. We define a general class of one-point algebraic-geometry codes encompassing, among others, Reed-Solomon codes, Hermitian codes and norm-trace codes. We show how for such codes the interpolation constraints in the Guruswami-Sudan list-decoder, can be rephrased using a module formulation. We then generalize an algorithm by Alekhnovich [2], and show how this can be used to efficiently solve the interpolation problem in this module reformulation. The family of codes we consider has a number of well-known members, for which the interpolation part of the Guruswami-Sudan list decoder has been studied previously. For such codes the complexity of the interpolation algorithm we propose, compares favorably to the complexity of known algorithms.
Citation: Peter Beelen, Kristian Brander. Efficient list decoding of a class of algebraic-geometry codes. Advances in Mathematics of Communications, 2010, 4 (4) : 485-518. doi: 10.3934/amc.2010.4.485
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##### References:
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