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We propose an effective version of the lift by derivation, an invariant that allows us to provide the classification of $ B(5,6,8) = RM(6, 8)/RM(4, 8) $. The main consequence is to establish that the covering radius of the Reed-Muller $ RM(4,8) $ is equal to 26.
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Gillot et al. (2023) studied this question.
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