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At the school, Mr. Hamming was known as a professor who felt mathematics should be fun.
The term usually applies to a single parity bit, although it could also be used to refer to a larger Hamming code.
Lecture 9: Bounds on the Volume of a Hamming Ball.
Ignoring both the man and the 'graph, Colonel Hamming crouched to inspect a little metal box on the floor next to the chair.
This triple repetition code is actually the simplest Hamming code with , since there are 2 parity bits, and data bit.
"Richard Hamming."
"We were first-class troublemakers," Mr. Hamming told Spectrum.
Like his codes, Mr. Hamming's digital filters became indispensable parts of the digital engineer's tool kit.
Mr. Hamming shunned a management role at Bell, transferring subordinate researchers to other jobs as soon as they were assigned to him.
The confusion arose from the similar Hamming function, named after Richard Hamming.
In fact, any binary Hamming code of the form Ham(2,q) is equivalent to a cyclic code when is even.
In addition to error correction, Mr. Hamming did pioneering work in digital filters while at Bell Labs.
To promote "New Year", a music video was directed by Alex Hamming and filmed in London, England.
However, the Hamming (7,4) and similar Hamming codes cannot distinguish between single-bit errors and two-bit errors.
The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code.
When the war ended, Mr. Hamming was offered a job at Bell Telephone Laboratories, but he remained at Los Alamos for six more months, until most of the other scientists had left.
"If you don't work on important problems, it's not likely that you'll do important work," was a favorite axiom of Mr. Hamming's, and he told Spectrum that his discoveries were the high point of his life.
One of Hamming's lessons is never trust without question someone who claims to be giving you highly accurate data to analyze - not because they're deliberately lying to you but because the data is never as accurate as people think.
For an n x n rook's graph the total number of vertices is simply and the total number of edges is ; in this case the graph is also known as a two-dimensional Hamming graph or a Latin square graph.
The development of the Hamming Codes was recognized in 1996 by the Eduard Rheim Foundation of Germany, which presented Mr. Hamming the $130,000 Eduard Rheim Award for Achievement in Technology.
Because a codeword is the only codeword in the Hamming ball centered at itself with radius , the two Hamming balls centered at two different codewords respectively with both radius do not overlap with each other.
Mr. Hamming was born on Feb. 11, 1915, in Chicago and earned a bachelor of science degree from the University of Chicago, a master's degree from the University of Nebraska and a doctorate from the University of Illinois, all in mathematics.
In 1947, while a researcher at Bell Telephone Laboratories, Mr. Hamming devised techniques for finding and correcting a single error in a string of data, as well as finding two errors and correcting one of them; the techniques became known as the Hamming Codes.
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