Locally decodable codes with 2 queries and polynomial identity testing for depth 3 circuits

In this work we study two, seemingly unrelated, notions. Locally Decodable Codes (LDCs) are codes that allow the recovery of each message bit from a constant number of entries of the codeword. Polynomial Identity Testing (PIT) is one of the fundamental problems of algebraic complexity: we are given a circuit computing a multivariate polynomial and we have to determine whether the polynomial is identically zero. We improve known results on locally decodable codes and on polynomial identity testing and show a relation between the two notions. In particular we obtain the following results:

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Zeev Dvir, Amir Shpilka
• Keywords: Algorithms, Decodable Codes, Message Bit, Polynomial Identity Testing, STOC 2005