Matching Vector Codes

An (r, , )-locally decodable code encodes a k-bit message x to an N-bit codeword C(x), such that for every i [k], the i-th message bit can be recovered with probability 1 - , by a randomized decoding procedure that queries only r bits, even if the codeword C(x) is corrupted in up to N locations. Recently a new class of locally decodable codes, based on families of vectors with restricted dot products has been discovered. We refer to those codes as Matching Vector (MV) codes. Several families of (r, , (r))-locally decodable MV codes have been obtained. While codes in those families were shorter than codes of earlier generations, they suffered from having large values of = (r). Codes with constant query complexity could only tolerate tiny amounts of error, and no MV codes of super-constant number of queries capable of tolerating a constant fraction of errors were known to exist. In this paper we develop a new view of matching vector codes and uncover certain similarities between MV co...

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Zeev Dvir, Parikshit Gopalan, Sergey Yekhanin
• Keywords: Decodable Codes, Decodable Mv Codes, ECCC 2010, MV Codes