Traditional Reed–Muller codes are binary codes, which means that messages and codewords are binary strings. When r and m are integers with 0 ≤ r ≤ m, the Reed–Muller code with parameters r and m is denoted as RM(r, m). When asked to encode a message consisting of k bits, where k = ∑ i = 0 r ( m i ) {\displaystyle \textstyle k=\sum _{i=0}^{r}{\binom {m}{i}}} holds, the RM(r, m) code produces a codeword consisting of 2m bits.