### LDPC codes associated with linear representations of geometries

(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:
http://hdl.handle.net/1854/LU-1969420

- author
- Peter Vandendriessche UGent
- organization
- year
- 2010
- 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.