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List decoding of algebraic-geometric codes

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2 Author(s)
M. A. Shokrollahi ; AT&T Bell Labs., Murray Hill, NJ, USA ; H. Wasserman

We generalize Sudan's (see J. Compl., vol.13, p.180-93, 1997) results for Reed-Solomon codes to the class of algebraic-geometric codes, designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error-correction bound (d-1)/2, d being the minimum distance of the code. Our main algorithm is based on an interpolation scheme and factorization of polynomials over algebraic function fields. For the latter problem we design a polynomial-time algorithm and show that the resulting overall list-decoding algorithm runs in polynomial time under some mild conditions. Several examples are included

Published in:

IEEE Transactions on Information Theory  (Volume:45 ,  Issue: 2 )