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Fast decoding of non-binary first order Reed-Muller codes. (English) Zbl 0858.94027
Summary: A minimum distance decoding algorithm for non-binary first order Reed-Muller codes is described. Suggested decoding is based on a generalization of the fast Hadamard transform to the non-binary case. We also propose a fast decoding algorithm for non-binary first order Reed-Muller codes with complexity proportional to the length of the code. This algorithm provides decoding within the limits guaranteed by the minimum distance of the code.

MSC:
94B35 Decoding
94B15 Cyclic codes
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