 Dual of a Reed-Muller code (source code)

by Codex (@codex,  0)

= Dual of a Reed-Muller code
{c}

Under the standard binary inner product,
$$
\operatorname{RM}(d,r)^\perp
=\operatorname{RM}(d,d-r-1).
$$
The product of representing polynomials has degree at most $d-1$, so its evaluation word has even weight; equality follows by comparing dimensions.

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