Hadamard code: Difference between revisions

Revision as of 15:04, 20 August 2015

Revision as of 15:05, 20 August 2015

Line 81:

==Constructions==

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 theory|coding theorists]], who analyzeanalyse extremal properties of codes, typically want the [[Block_code#The_rate_R|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.

===Construction using inner products===