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Reed-Muller code

Bar product of binary linear codes

{c}

For $0<r<d$,
$$
\operatorname{RM}(d,r)
=\operatorname{RM}(d-1,r)
\mid\operatorname{RM}(d-1,r-1).
$$
Consequently
$$
\dim\operatorname{RM}(d,r)=\sum_{j=0}^r\binom dj.
$$

Reed-Muller bar-product recursion

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Reed-Muller bar-product recursion

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Reed-Muller bar-product recursion

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