Labcoin bitcoin wiki is the approved revision of this page, as well as being the most recent. In 1971, the code was used to transmit photos of Mars back to Earth from the NASA space probe Mariner 9.
Hadamard matrices, which are not necessarily of Sylvester type. In general, such a code is not linear. Such codes were first constructed by R. The Hadamard code is a locally decodable code, which provides a way to recover parts of the original message with high probability, while only looking at a small fraction of the received word. This gives rise to applications in computational complexity theory and particularly in the design of probabilistically checkable proofs. Hadamard code is referred to as Walsh Code, and is used to define individual communication channels.
Hadamard code is the name that is most commonly used for this code in the literature. The Hadamard code is based on Hadamard matrices, and while there are many different Hadamard matrices that could be used here, normally only Sylvester’s construction of Hadamard matrices is used to obtain the codewords of the Hadamard code. James Joseph Sylvester developed his construction of Hadamard matrices in 1867, which actually predates Hadamard’s work on Hadamard matrices. Hence the name Hadamard code is not undisputed and sometimes the code is called Walsh code, honoring the American mathematician Joseph Leonard Walsh. The data words used during this mission were 6 bits long, which represented 64 grayscale values. Instead of using a repetition code, a Hadamard code was used.
The efficient decoding algorithm was an important factor in the decision to use this code. The circuitry used was called the “Green Machine”. It employed the fast Fourier transform which can increase the decoding speed by a factor of three. While all Hadamard codes are based on Hadamard matrices, the constructions differ in subtle ways for different scientific fields, authors, and uses.