On Representations of Algebraic-Geometric Codes
نویسندگان
چکیده
We show that all algebraic-geometric codes possess a succinct representation that allows for the list decoding algorithms of [9, 6] 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.
منابع مشابه
On Representations of Algebraic-Geometric Codes for List Decoding
We show that all algebraic-geometric codes possess a succinct representation that allows for the list decoding algorithms of [15, 7] 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...
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تاریخ انتشار 1998