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Codes on finite geometries

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4 Author(s)
Tang, H. ; PMC-Sierra Inc., Portland, OR, USA ; Jun Xu ; Shu Lin ; Abdel-Ghaffar, K.A.S.

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.

Published in:

Information Theory, IEEE Transactions on  (Volume:51 ,  Issue: 2 )