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• W2068593329 abstract "We consider Reed-Solomon (RS) codes whose evaluation points belong to a subfield, and give a linear-algebraic list decoding algorithm that can correct a fraction of errors approaching the code distance, while pinning down the candidate messages to a well-structured affine space of dimension a constant factor smaller than the code dimension. By pre-coding the message polynomials into a subspace-evasive set, we get a Monte Carlo construction of a subcode of Reed-Solomon codes that can be list decoded from a fraction (1-R-ε) of errors in polynomial time (for any fixed ε > 0) with a list size of O(1/ε). Our methods extend to algebraic-geometric (AG) codes, leading to a similar claim over constant-sized alphabets. This matches parameters of recent results based on folded variants of RS and AG codes. but our construction here gives subcodes of Reed-Solomon and AG codes themselves (albeit with restrictions on the evaluation points)." @default.
• W2068593329 created "2016-06-24" @default.
• W2068593329 creator A5019628468 @default.
• W2068593329 creator A5068388812 @default.
• W2068593329 date "2013-06-01" @default.
• W2068593329 modified "2023-10-16" @default.
• W2068593329 title "List decoding reed-solomon, algebraic-geometric, and gabidulin subcodes up to the singleton bound" @default.
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• W2068593329 doi "https://doi.org/10.1145/2488608.2488715" @default.
• W2068593329 hasPublicationYear "2013" @default.
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