simplex codes

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simplex codes 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.