From irreducible representations to locally decodable codes

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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.
Klim Efremenko
Added 28 Sep 2012
Updated 28 Sep 2012
Type Journal
Year 2012
Where STOC
Authors Klim Efremenko
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