Extractors from Reed-Muller Codes

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Extractors from Reed-Muller Codes (2001)

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by Amnon Ta-shma , David Zuckerman , Shmuel Safra

Venue:	In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science
Citations:	39 - 4 self

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@INPROCEEDINGS{Ta-shma01extractorsfrom,
    author = {Amnon Ta-shma and David Zuckerman and Shmuel Safra},
    title = {Extractors from Reed-Muller Codes},
    booktitle = {In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science},
    year = {2001},
    pages = {638--647},
    publisher = {IEEE}
}

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Abstract

Finding explicit extractors is an important derandomization goal that has received a lot of attention in the past decade. This research has focused on two approaches, one related to hashing and the other to pseudorandom generators. A third view, regarding extractors as good error correcting codes, was noticed before. Yet, researchers had failed to build extractors directly from a good code, without using other tools from pseudorandomness. We succeed in constructing an extractor directly from a Reed-Muller code. To do this, we develop a novel proof technique. Furthermore, our construction is the first and only construction with degree close to linear. In contrast, the best previous constructions had brought the log of the degree within a constant of optimal, which gives polynomial degree. This improvement is important for certain applications. For example, it follows that approximating the VC dimension to within a factor of N

Keyphrases

reed-muller code third view past decade vc dimension previous construction degree close good code good error novel proof technique certain application important derandomization goal explicit extractor polynomial degree

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