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


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.


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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