Bar product (original) (raw)

In information theory, the bar product of two linear codes C2 ⊆ C1 is defined as where (a | b) 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 (d, r) code in terms of the Reed–Muller codes RM (d − 1, r) and RM (d − 1, r − 1). The bar product is also referred to as the | u | u+v | constructionor (u | u + v) construction.