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LDPC codes associated with linear representations of geometries

Peter Vandendriessche UGent (2010) ADVANCES IN MATHEMATICS OF COMMUNICATIONS. 4(3). p.405-417
abstract
We look at low density parity check codes over a finite field K associated with finite geometries T*(2) (K), where K is any subset of PG(2, q), with q = p(h), p not equal char K. This includes the geometry LU(3, q)(D), the generalized quadrangle T*(2)(K) with K a hyperoval, the affine space AG(3, q) and several partial and semi-partial geometries. In some cases the dimension and/or the code words of minimum weight are known. We prove an expression for the dimension and the minimum weight of the code. We classify the code words of minimum weight. We show that the code is generated completely by its words of minimum weight. We end with some practical considerations on the choice of K.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
linear representation, finite geometry, linear codes, LDPC codes, dimension, minimum distance
journal title
ADVANCES IN MATHEMATICS OF COMMUNICATIONS
Adv. Math. Commun.
volume
4
issue
3
pages
405 - 417
Web of Science type
Article
Web of Science id
000280383000008
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.544 (2010)
JCR rank
166/235 (2010)
JCR quartile
3 (2010)
ISSN
1930-5346
DOI
10.3934/amc.2010.4.405
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1969420
handle
http://hdl.handle.net/1854/LU-1969420
date created
2011-12-19 03:27:53
date last changed
2018-06-22 13:46:44
@article{1969420,
  abstract     = {We look at low density parity check codes over a finite field K associated with finite geometries T*(2) (K), where K is any subset of PG(2, q), with q = p(h), p not equal char K. This includes the geometry LU(3, q)(D), the generalized quadrangle T*(2)(K) with K a hyperoval, the affine space AG(3, q) and several partial and semi-partial geometries. In some cases the dimension and/or the code words of minimum weight are known. We prove an expression for the dimension and the minimum weight of the code. We classify the code words of minimum weight. We show that the code is generated completely by its words of minimum weight. We end with some practical considerations on the choice of K.},
  author       = {Vandendriessche, Peter},
  issn         = {1930-5346},
  journal      = {ADVANCES IN MATHEMATICS OF COMMUNICATIONS},
  keyword      = {linear representation,finite geometry,linear codes,LDPC codes,dimension,minimum distance},
  language     = {eng},
  number       = {3},
  pages        = {405--417},
  title        = {LDPC codes associated with linear representations of geometries},
  url          = {http://dx.doi.org/10.3934/amc.2010.4.405},
  volume       = {4},
  year         = {2010},
}

Chicago
Vandendriessche, Peter. 2010. “LDPC Codes Associated with Linear Representations of Geometries.” Advances in Mathematics of Communications 4 (3): 405–417.
APA
Vandendriessche, P. (2010). LDPC codes associated with linear representations of geometries. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 4(3), 405–417.
Vancouver
1.
Vandendriessche P. LDPC codes associated with linear representations of geometries. ADVANCES IN MATHEMATICS OF COMMUNICATIONS. 2010;4(3):405–17.
MLA
Vandendriessche, Peter. “LDPC Codes Associated with Linear Representations of Geometries.” ADVANCES IN MATHEMATICS OF COMMUNICATIONS 4.3 (2010): 405–417. Print.