Abstract:
A list decoding algorithm is designed for the first-order binary Reed–Muller codes
of length $n$ that reconstructs all codewords located within the ball of radius
$\frac n2(1-\varepsilon)$ about the received vector and has the complexity of
$\mathcal O(n\ln^2(\min\{\varepsilon^{-2},n\}))$ binary operations.
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