Let n be a fixed positive integer, and consider an
alphabet consisting of the numbers 1, 2, … , n. With
this alphabet form all possible k-letter words
(a
1
a
2 … a
k
), where k is also fixed. There are
evidently n
k
such words in all.
An Hadamard matrix H is an n by n matrix all of whose entries are +1 or -1 which satisfies HH T = n J, H T being the transpose of H. The order n is necessarily 1, 2 or 42, with t a positive integer. R. E. A. C. Paley
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