## Abstract

The wide use of first order Reed-Muller codes (RM-1) in communications is determinated by their optimality and by the existence of fast algorithms for their decoding. The correlation algorithm for decoding RM-1 code was based on the algorithm of fast Walsh-Hadamard transform (FWHT) with complexity n log n where n is the RM-1 code length. We describe the new simplified algorithm which realizes the code distance and can correct a considerable number of errors of a larger weight. Correcting properties of this algorithm in the Gaussian channel are investigated by comparing it with the maximum likelihood algorithm

Original language | English |
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Pages (from-to) | 189-201 |

Number of pages | 13 |

Journal | Problems of control and information theory |

Volume | 14 |

Issue number | 3 |

State | Published - 1985 |