Fast decoding of non-binary first order Reed-Muller codes |
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Authors: | Alexey E Ashikhmin Simon N Litsyn |
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Affiliation: | (1) Institute for Problems of Information Transmission, Ermolovoy 19, GSP-4, 101447 Moscow, Russia;(2) Department of Electrical Engineering -Systems, Tel-Aviv University, 69978 Ramat Aviv, Israel |
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Abstract: | 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.Partly supported by the Guastallo Fellowship. This work was presented in part at the 9th International Symposium Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, New Orleans, USA, October 1991 |
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Keywords: | Fast decoding algorithms Reed-Muller codes |
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