Zeev Dvir, Parikshit Gopalan, and Sergey Yekhanin
Starting with the work of Yekhanin, a new family of locally decodable codes based on vectors with restricted dot products has been discovred. We refer to such codes as Matching Vector Codes. In this work, we present a new "polynomial" view of these codes, which uncovers certain similarities to the classical Reed Muller codes. We use this to give decoding algorithms for such codes that can correct a constant fraction of errors. We also present lower bounds on the length of any such code.
In FOCS 2010
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