Finite-geometry LDPC (FG-LDPC) code[1] 


LDPC code whose parity-check matrix is the incidence matrix of points and hyperplanes in either a Euclidean or a projective geometry. Such codes are called Euclidean-geometry LDPC (EG-LDPC) and projective-geometry LDPC (PG-LDPC), respectively. Such constructions have been generalized to incidence matrices of hyperplanes of different dimensions [2].




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Heng Tang et al., “Codes on finite geometries”, IEEE Transactions on Information Theory 51, 572 (2005) DOI
“Latin Squares and their Applications”, (2015) DOI
R. E. Blahut, Algebraic Codes for Data Transmission (Cambridge University Press, 2003) DOI
P. K. Sarvepalli, A. Klappenecker, and M. Rötteler, “Asymmetric quantum codes: constructions, bounds and performance”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, 1645 (2009) DOI
S. A. Aly, “A Class of Quantum LDPC Codes Constructed From Finite Geometries”, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference (2008) arXiv:0712.4115 DOI
J. Farinholt, “Quantum LDPC Codes Constructed from Point-Line Subsets of the Finite Projective Plane”, (2012) arXiv:1207.0732
B. Audoux and A. Couvreur, “On tensor products of CSS Codes”, (2018) arXiv:1512.07081
S. Miao et al., “A Joint Code and Belief Propagation Decoder Design for Quantum LDPC Codes”, (2024) arXiv:2401.06874
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Zoo Code ID: pg_ldpc

Cite as:
“Finite-geometry LDPC (FG-LDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.
@incollection{eczoo_pg_ldpc, title={Finite-geometry LDPC (FG-LDPC) code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Finite-geometry LDPC (FG-LDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.