On representations of algebraic-geometry codes

Authors:
V. Guruswami;M. Sudan
Affiliations:
Lab. for Comput. Sci., MIT, Cambridge, MA;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

Citing 0
Cited 7

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Abstract

We show that all algebraic-geometric codes possess a succinct representation that allows for list decoding algorithms to run in polynomial time. We do this by presenting a root-finding algorithm for univariate polynomials over function fields when their coefficients lie in finite-dimensional linear spaces, and proving that there is a polynomial size representation, given which the root-finding algorithm runs in polynomial time