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.

PDF file

In  FOCS 2010

Publisher  IEEE
© 2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. http://www.ieee.org/

Details