Note that the Walsh functions (usually denoted wal) consist alternatively of even and odd functions (usually denoted cal and sal by analogy with cos and sin). Furthermore, within the set of 2n functions there is one function of zero sequency, one of (normalized) sequency 2n–1, and one pair (odd and even) of each (normalized) sequency from 1 to 2n–1 – 1.
A set of Walsh functions corresponds, with some permutation of columns, to a Reed–Muller code and, with a column deleted, to a simplex code. See also Hadamard matrices.
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