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Designs, Codes and Cryptography

, Volume 54, Issue 3, pp 287–297 | Cite as

Some low-density parity-check codes derived from finite geometries

  • Peter Vandendriessche
Article

Abstract

We look at low-density parity-check codes over a finite field \({\mathbb{K}}\) associated with finite geometries \({T_2^*(\mathcal{K})}\), where \({\mathcal{K}}\) is a sufficiently large k-arc in PG(2, q), with q = p h . The code words of minimum weight are known. With exception of some choices of the characteristic of \({\mathbb{K}}\) we compute the dimension of the code and show that the code is generated completely by its code words of minimum weight.

Keywords

LDPC Error rate Dimension Linear representation Generalized quadrangle LU(3, q

Mathematics Subject Classification (2000)

05B25 05C38 05C50 51E12 51E21 51E22 94B27 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.TorhoutBelgium

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