TY - GEN

T1 - From irreducible representations to locally decodable codes

AU - Efremenko, Klim

PY - 2012/6/26

Y1 - 2012/6/26

N2 - A q-query Locally Decodable Code (LDC) is an error-correcting code that allows to read any particular symbol of the message by reading only q symbols of the codeword even if the codeword is adversary 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 g 1,g 2,..., g q in G such that there exists a linear combination of matrices ρ(g i) that is of rank one, then we can construct a q-query Locally Decodable Code C:V → double-struck F G. We show the potential of this approach by constructing constant query LDCs of sub-exponential length matching the best known constructions.

AB - A q-query Locally Decodable Code (LDC) is an error-correcting code that allows to read any particular symbol of the message by reading only q symbols of the codeword even if the codeword is adversary 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 g 1,g 2,..., g q in G such that there exists a linear combination of matrices ρ(g i) that is of rank one, then we can construct a q-query Locally Decodable Code C:V → double-struck F G. We show the potential of this approach by constructing constant query LDCs of sub-exponential length matching the best known constructions.

KW - locally decodable codes

KW - representation theory

UR - http://www.scopus.com/inward/record.url?scp=84862624759&partnerID=8YFLogxK

U2 - 10.1145/2213977.2214008

DO - 10.1145/2213977.2214008

M3 - Conference contribution

AN - SCOPUS:84862624759

SN - 9781450312455

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 327

EP - 337

BT - STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing

T2 - 44th Annual ACM Symposium on Theory of Computing, STOC '12

Y2 - 19 May 2012 through 22 May 2012

ER -