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Richard Hamming in computer science, "The Unreasonable Effectiveness of Mathematics". [5] Arthur Lesk in molecular biology, "The Unreasonable Effectiveness of Mathematics in Molecular Biology". [6] Peter Norvig in artificial intelligence, "The Unreasonable Effectiveness of Data" [7] Max Tegmark in physics, "The Mathematical Universe". [8]
See Hamming code for an example of an error-correcting code. Parity bit checking is used occasionally for transmitting ASCII characters, which have 7 bits, leaving the 8th bit as a parity bit. For example, the parity bit can be computed as follows. Assume Alice and Bob are communicating and Alice wants to send Bob the simple 4-bit message 1001.
This code has minimal Hamming distance 15 and corrects 7 errors. It has 1 data bit and 14 checksum bits. ... Definition. Fix a finite field (), ...
Created the fields of error-correcting code, Hamming code, Hamming matrix, the Hamming window, Hamming numbers, sphere-packing (or Hamming bound), and the Hamming distance; [28] [29] established the concept of perfect code [30] [31] 1956, 1958, 1974 Händler, Wolfgang
In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other.
The Hamming(7,4) code may be written as a cyclic code over GF(2) with generator + +. In fact, any binary Hamming code of the form Ham(r, 2) is equivalent to a cyclic code, [3] and any Hamming code of the form Ham(r,q) with r and q-1 relatively prime is also equivalent to a cyclic code. [4]
Convolutional codes are processed on a bit-by-bit basis. They are particularly suitable for implementation in hardware, and the Viterbi decoder allows optimal decoding. Block codes are processed on a block-by-block basis. Early examples of block codes are repetition codes, Hamming codes and multidimensional parity-check codes.
In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. . Given a discrete random variable , which takes values in the set and is distributed according to : [,], the entropy is ():= (), where denotes the sum over the variable's possible va