# Seminar: April 9

## Klim Efremenko, IAS

## From Irreducible Representations to Locally Decodable Codes

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.

In this talk we present a new approach for the construction of LDCs from the representation theory. We show that if there exists an irreducible representation (\rho, V) of the 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 \to F^G.

We will show that both matching vector codes and Reed-Muller codes fall in this framework.

No prior knowledge in representation theory will be assumed.