Fast decoding of non-binary first order Reed-Muller codes

Alexey E. Ashikhmin; Simon N. Litsyn

doi:10.1007/BF01195535

Fast decoding of non-binary first order Reed-Muller codes

Alexey E. Ashikhmin^*, Simon N. Litsyn

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	299-308
Number of pages	10
Journal	Applicable Algebra in Engineering, Communications and Computing
Volume	7
Issue number	4
DOIs	https://doi.org/10.1007/BF01195535
State	Published - 1996

Keywords

Fast decoding algorithms
Reed-Muller codes

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10.1007/BF01195535

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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.",

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AU - Litsyn, Simon N.

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AB - 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.

KW - Fast decoding algorithms

KW - Reed-Muller codes

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ER -

Fast decoding of non-binary first order Reed-Muller codes

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Keywords

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