Construction
While all Hadamard codes are based on Hadamard matrices, the constructions differ in subtle ways for different scientific fields, authors, and uses. Engineers, who use the codes for data transmission, and coding theorists, who analyze extremal properties of codes, typically want the rate of the code to be as high as possible, even if this means that the construction becomes mathematically slightly less elegant. On the other hand, for many applications of Hadamard codes in theoretical computer science it is not so important to achieve the optimal rate, and hence simpler constructions of Hadamard codes are preferred since they can be analyzed more elegantly.
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