From irreducible representations to locally decodable codes

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publicationSTOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing
Pages327-337
Number of pages11
DOIs
StatePublished - 26 Jun 2012
Externally publishedYes
Event44th Annual ACM Symposium on Theory of Computing, STOC '12 - New York, NY, United States
Duration: 19 May 201222 May 2012

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference44th Annual ACM Symposium on Theory of Computing, STOC '12
Country/TerritoryUnited States
CityNew York, NY
Period19/05/1222/05/12

Keywords

  • locally decodable codes
  • representation theory

Cite this