{"id":159771,"date":"2010-10-01T00:00:00","date_gmt":"2010-10-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/matching-vector-codes\/"},"modified":"2018-10-16T19:58:05","modified_gmt":"2018-10-17T02:58:05","slug":"matching-vector-codes","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/matching-vector-codes\/","title":{"rendered":"Matching Vector Codes"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Starting with the work of Yekhanin, a new family of locally decodable codes based on vectors with restricted dot products has been discovered. We refer to such codes as Matching Vector Codes. In this work, we present a new &#8220;polynomial&#8221; 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.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Starting with the work of Yekhanin, a new family of locally decodable codes based on vectors with restricted dot products has been discovered. We refer to such codes as Matching Vector Codes. In this work, we present a new &#8220;polynomial&#8221; view of these codes, which uncovers certain similarities to the classical Reed Muller codes. 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