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.
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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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Ashikhmin, A.E., Litsyn, S.N. Fast decoding of non-binary first order Reed-Muller codes. AAECC 7, 299–308 (1996). https://doi.org/10.1007/BF01195535
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DOI: https://doi.org/10.1007/BF01195535