From irreducible representations to locally decodable codes

Locally Decodable Code (LDC) is a code that encodes a message in a way that one can decode any particular symbol of the message by reading only a constant number of locations, even if a constant fraction of the encoded message is adversarially corrupted. In this paper we present a new approach for the construction of LDCs. We show that if there exists an irreducible representation (ρ, V ) of G and q elements g1, g2, . . . , gq in G such that there exists a linear combination of matrices ρ(gi) that is of rank one, then we can construct a q-query Locally Decodable Code C : V → FG. We show the potential of this approach by constructing constant query LDCs of subexponential length matching the parameters of the best known constructions.

• Type: Journal
• Year: 2012
• Where: STOC
• Authors: Klim Efremenko
• Keywords: Algorithms, Irreducible Representation, Ldcs, Rank One, STOC 2012