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In information theory, the bar product of two linear codes C2 ⊆ C1 is defined as

where denotes the concatenation of a and b. If the code words in C1 are of length n, then the code words in C1 | C2 are of length 2n.

The bar product is an especially convenient way of expressing the Reed–Muller RM  code in terms of the Reed–Muller codes RM  and RM .

The bar product is also referred to as the | u | u+v | constructionor construction.

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