A family of linear error-correcting or error-detecting block codes, easily implemented as polynomial codes (by means of shift registers). Considered as (n, k) codes (see block code), they have codeword length n = qk − 1 Binary simplex codes have a minimum Hamming distance equal to 2k-1. They can be regarded as Reed-Muller codes shortened by one digit, and are identical with the m-sequences of length 2k − 1, together with the zero word. They are so called because their codewords form a simplex in Hamming space.
n = qk − 1