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Elements of Algebraic Coding Systems by Valdemar Cardoso da Rocha, Jr.

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Chapter 11

MAJORITY LOGIC DECODING

11.1 Introduction

Majority logic decoding is a well-established branch of the theory of error-correcting codes. It draws heavily from the theory of finite geometries, e.g., Euclidean and projective geometries, both for the construction of codes and for their decoding. In general the resulting codes are not very powerful but their decoders are both simple and very fast. For practical applications most attention is given to either cyclic block codes or to convolutional codes of rate 1/n or (n − 1)/n because of the resulting simplified decoders.

11.2 One-step majority logic decoding

Any (n, k) linear block code C, over GF(q), has a parity-check matrix H and the codewords c, c C, satisfy cHT = 0. Denoting the ...

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