New descriptions of the weighted Reed-Muller codes and the homogeneous Reed-Muller codes

Published 4 Jan 2017 in cs.IT and math.IT | (1701.01059v1)

Abstract: We give a description of the weighted Reed-Muller codes over a prime field in a modular algebra. A description of the homogeneous Reed-Muller codes in the same ambient space is presented for the binary case. A decoding procedure using the Landrock-Manz method is developed.

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