Codes and designs related to lifted MRD codes

Natalia Silberstein; Tuvi Etzion

doi:10.1109/ISIT.2011.6033969

Codes and designs related to lifted MRD codes

Natalia Silberstein, Tuvi Etzion

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

13 Scopus citations

Abstract

The lifted maximum rank distance codes are considered. It is shown that these codes form structures which are transversal designs and also have some similarity to q-analog of transversal designs. Upper bounds on the sizes of codes which contain the lifted maximum rank distance codes are derived. A new construction for codes which attain one of these upper bounds is given. Low density parity check codes are derived from the lifted maximum rank distance codes and some of these codes are quasi-cyclic codes attaining the Griesmer bound.

Original language	English
Title of host publication	2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages	2288-2292
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2011.6033969
State	Published - 26 Oct 2011
Externally published	Yes
Event	2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation Duration: 31 Jul 2011 → 5 Aug 2011

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8104

Conference

Conference	2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Country/Territory	Russian Federation
City	St. Petersburg
Period	31/07/11 → 5/08/11

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.2011.6033969

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title = "Codes and designs related to lifted MRD codes",

abstract = "The lifted maximum rank distance codes are considered. It is shown that these codes form structures which are transversal designs and also have some similarity to q-analog of transversal designs. Upper bounds on the sizes of codes which contain the lifted maximum rank distance codes are derived. A new construction for codes which attain one of these upper bounds is given. Low density parity check codes are derived from the lifted maximum rank distance codes and some of these codes are quasi-cyclic codes attaining the Griesmer bound.",

author = "Natalia Silberstein and Tuvi Etzion",

year = "2011",

month = oct,

day = "26",

doi = "10.1109/ISIT.2011.6033969",

language = "English",

isbn = "9781457705953",

series = "IEEE International Symposium on Information Theory - Proceedings",

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booktitle = "2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011",

note = "2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 ; Conference date: 31-07-2011 Through 05-08-2011",

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Silberstein, N & Etzion, T 2011, Codes and designs related to lifted MRD codes. in 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011., 6033969, IEEE International Symposium on Information Theory - Proceedings, pp. 2288-2292, 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011, St. Petersburg, Russian Federation, 31/07/11. https://doi.org/10.1109/ISIT.2011.6033969

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AU - Silberstein, Natalia

AU - Etzion, Tuvi

PY - 2011/10/26

Y1 - 2011/10/26

N2 - The lifted maximum rank distance codes are considered. It is shown that these codes form structures which are transversal designs and also have some similarity to q-analog of transversal designs. Upper bounds on the sizes of codes which contain the lifted maximum rank distance codes are derived. A new construction for codes which attain one of these upper bounds is given. Low density parity check codes are derived from the lifted maximum rank distance codes and some of these codes are quasi-cyclic codes attaining the Griesmer bound.

AB - The lifted maximum rank distance codes are considered. It is shown that these codes form structures which are transversal designs and also have some similarity to q-analog of transversal designs. Upper bounds on the sizes of codes which contain the lifted maximum rank distance codes are derived. A new construction for codes which attain one of these upper bounds is given. Low density parity check codes are derived from the lifted maximum rank distance codes and some of these codes are quasi-cyclic codes attaining the Griesmer bound.

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U2 - 10.1109/ISIT.2011.6033969

DO - 10.1109/ISIT.2011.6033969

M3 - Conference contribution

AN - SCOPUS:80054812556

SN - 9781457705953

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2288

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BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

Y2 - 31 July 2011 through 5 August 2011

ER -

Codes and designs related to lifted MRD codes

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