From irreducible representations to locally decodable codes

Klim Efremenko

doi:10.1145/2213977.2214008

From irreducible representations to locally decodable codes

Klim Efremenko

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	English
Title of host publication	STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing
Pages	327-337
Number of pages	11
DOIs	https://doi.org/10.1145/2213977.2214008
State	Published - 26 Jun 2012
Externally published	Yes
Event	44th Annual ACM Symposium on Theory of Computing, STOC '12 - New York, NY, United States Duration: 19 May 2012 → 22 May 2012

Publication series

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

Conference

Conference	44th Annual ACM Symposium on Theory of Computing, STOC '12
Country/Territory	United States
City	New York, NY
Period	19/05/12 → 22/05/12

Keywords

locally decodable codes
representation theory

ASJC Scopus subject areas

Software

Access to Document

10.1145/2213977.2214008

Cite this

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title = "From irreducible representations to locally decodable codes",

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.",

keywords = "locally decodable codes, representation theory",

author = "Klim Efremenko",

year = "2012",

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doi = "10.1145/2213977.2214008",

language = "English",

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series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

pages = "327--337",

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note = "44th Annual ACM Symposium on Theory of Computing, STOC '12 ; Conference date: 19-05-2012 Through 22-05-2012",

}

Efremenko, K 2012, From irreducible representations to locally decodable codes. in STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 327-337, 44th Annual ACM Symposium on Theory of Computing, STOC '12, New York, NY, United States, 19/05/12. https://doi.org/10.1145/2213977.2214008

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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

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U2 - 10.1145/2213977.2214008

DO - 10.1145/2213977.2214008

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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 -

From irreducible representations to locally decodable codes

Abstract

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Conference

Keywords

ASJC Scopus subject areas

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