Codes on finite geometries |
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Authors: | Tang H Xu J Lin S Abdel-Ghaffar KAS |
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Affiliation: | PMC-Sierra Inc., Portland, OR, USA; |
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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. |
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