Decoding by Sequential Code Reduction

A general decoding method for cyclic codes is presented which gives promise of substantially reducing the complexity of decoders at the cost of a modest increase in decoding time (or delay). Significant reductions in decoder complexity for binary cyclic finite-geometry codes are demonstrated, and two decoding options for the Golay code are presented

Generalized Finite-Geometry Codes

A technique is presented for constructing cyclic codes that retain many of the combinatorial properties of finite-geometry codes, but are often superior to geometry codes. It is shown that L-step orthogonalization is applicable to certain subclasses of these codes

Mathematical structures for decoding projective geometry codes

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Some new results on majority-logic codes for correction of random errors

The main advantages of random error-correcting majority-logic codes and majority-logic decoding in general are well known and two-fold. Firstly, they offer a partial solution to a classical coding theory problem, that of decoder complexity. Secondly, a majority-logic decoder inherently corrects many more random error patterns than the minimum distance of the code implies is possible. The solution to the decoder complexity is only a partial one because there are circumstances under which a majority-logic decoder is too complex and expensive to implement. [Continues.