Hadamard code: Difference between revisions

Revision as of 23:50, 4 January 2023

Revision as of 21:44, 14 August 2023

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[[File:Hadamard-Code.svg|thumb|250 px|Matrix of the Augmented Hadamard code [32, 6, 16] for the [[Reed–Muller code]] (1, 5) of the NASA space probe [[Mariner 9]]]]

[[File:MultigradeVariadic operatorlogical 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]] named after [[Jacques Hadamard]] 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]].<ref name="Malek_2006"/> 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]].