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docs/src/Classical/new_codes_from_old.md

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The direct sum code has generator matrix `G1 ⊕ G2` and parity-check matrix `H1 ⊕ H2`.
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```@docs
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```
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The generator matrix of the (direct) product code is the kronecker product of the generator matrices of the inputs.
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```@docs
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×
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```
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The parity-check matrix of the tensor product code is the kronecker product of the parity-check matrices of the inputs.
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There is some debate on how to define this product. This is known to often be the full ambient space.
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```@docs
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entrywise_product_code
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```
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```@docs
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/
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```
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`juxtaposition` is representation dependent and therefore works on the potentially over-complete generator matrices, not on the standard form.
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```@docs
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juxtaposition

docs/src/Tutorials/Message Passing.md

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Logical errors were equally distributed among the cosets and only occurred on odd-distance codes.
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julia> x = -20:.05:20; y = [abs(atanh(tanh(x)) - x) for x in x]; y2 = [exp(2abs(x)) / 2^56 for x in x]; plot(x, [replace(y, 0.0 => 1e-21) y2], ylims = (1e-20, 1), yscale = :log10, linewidth = 0.5, label = ["abs(atanh(tanh(x)) - x)" "exp(2abs(x)) / 2^56"])
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p = 1 - 1/(1 + exp(LLR)) if LLR = log(p / (1 - p))

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