Klim Efremenko (Tel-Aviv University)
Wednesday, 20.6.2012, 12:30
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 talk we will show connection between LDC and a representation theory.
We show that if there exists an irreducible representation (\rho, V) of a group G and q elements g_1,g_2,..., g_q
in $G$ such that there exists a linear combination of matrices \rho(g_i) that is of rank one, then we can construct a $q$-query Locally Decodable Code C:V-> F^G.
We show the potential of this approach by constructing constant query LDCs of sub-exponential length matching the parameters of the best known constructions.
No prior knowledge in representation theory will be assumed.