Hadamard code: Difference between revisions

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[[File:Multigrade operator XOR.svg|thumb|250px|[[Exclusive or|XOR]] operations<br>Here the white fields stand for 0<br>and the red fields for 1]]

The '''Hadamard code''' is an [[error-correcting code]] that is used for [[error detection and correction]] when transmitting messages over very noisy or unreliable channels. In 1971, the code was used to transmit photos of Mars back to Earth from the NASA space probe [[Mariner 9]]{{citation<ref>http://www.mcs.csueastbay.edu/~malek/TeX/Hadamard.pdf</ref>. needed|date=JanuaryBecause 2015}}of its unique mathematical properties, the Hadamard code is not only used by engineers, but also intensely studied in [[coding theory]], [[mathematics]], and [[theoretical computer science]].

Because of its unique mathematical properties, the Hadamard code is not only used by engineers, but also intensely studied in [[coding theory]], [[mathematics]], and [[theoretical computer science]].

The Hadamard code is named after the French mathematician [[Jacques Hadamard]].

It is also known under the names '''Walsh code''', '''Walsh family''',<ref>See, e.g., {{Harvtxt|Amadei|Manzoli|Merani|2002}}</ref> and '''Walsh–Hadamard code'''<ref>See, e.g., {{Harvtxt|Arora|Barak|2009|loc=Section 19.2.2}}.</ref> in recognition of the American mathematician [[Joseph Leonard Walsh]].