Codes on finite geometries

Authors:
H. Tang;J. Xu;S. Lin;K. A.S. Abdel-Ghaffar
Affiliations:
PMC-Sierra Inc., Portland, OR, USA;-;-;-
Venue:
IEEE Transactions on Information Theory
Year:
2005

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Abstract

New algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented. The new construction methods result in a class of multistep majority-logic decodable codes and three classes of low-density parity-check (LDPC) codes. Decoding methods for the class of majority-logic decodable codes, and a class of codes that perform well with iterative decoding in spite of having many cycles of length 4 in their Tanner graphs, are presented. Most of the codes constructed can be either put in cyclic or quasi-cyclic form and hence their encoding can be implemented with linear shift registers.