highest possible rate for codes with their block length and minimum distance of three. Richard W. Hamming invented Hamming codes in 1950 as a way of automatically...

family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950. At the time, Hamming worked...

include the Hamming code (which makes use of a Hamming matrix), the Hamming window, Hamming numbers, sphere-packing (or Hamming bound), Hamming graph concepts...

capability of the code. The Hamming distance is named after Richard Hamming, who introduced the concept in his fundamental paper on Hamming codes, Error detecting...

Hamming may refer to: Richard Hamming (1915–1998), American mathematician Hamming(7,4), in coding theory, a linear error-correcting code Overacting, or...

computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing...

code is a sequence of dual Hamming codes. Some examples of linear codes include: Repetition codes Parity codes Cyclic codes Hamming codes Golay code,...

mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code. FEC can be applied...

Hamming, whose work has had many implications for computer science and telecommunications. His contributions include the invention of the Hamming code...

. In fact, any binary Hamming code of the form Ham(r, 2) is equivalent to a cyclic code, and any Hamming code of the form Ham(r,q) with r and q-1 relatively...

Hadamard code while the second is called the augmented Hadamard code. The Hadamard code is unique in that each non-zero codeword has a Hamming weight of...

classical binary [7,4,3] Hamming code to correct for both qubit flip errors (X errors) and phase flip errors (Z errors). The Steane code encodes one logical...

equivalent to Hamming weight in the binary case, in 1954. Hamming weight is used in several disciplines including information theory, coding theory, and...

extended binary Golay code, all code words have Hamming weights of 0, 8, 12, 16, or 24. Code words of weight 8 are called octads and code words of weight 12...

Neil Sloane. The binary lexicographic codes are linear codes, and include the Hamming codes and the binary Golay codes. A lexicode of length n and minimum...

block code to each other, such as its rate and its ability to detect and correct errors. Examples of block codes are Reed–Solomon codes, Hamming codes, Hadamard...

related to the (extended) Hamming code H(8,4) and can, in fact, be constructed from it. The Hamming code H(8,4) is a binary code of length 8 and rank 4;...

subspace of its Hamming space, it is called a linear code. A typical example of linear code is the Hamming code. Codes defined via a Hamming space necessarily...

practice, stripes data at the bit (rather than block) level, and uses a Hamming code for error correction. The disks are synchronized by the controller to...

faster than that of Hamming error correction scheme. Space satellite systems often use TMR, although satellite RAM usually uses Hamming error correction...

error-detecting and error-correcting codes. He invented the concepts known as Hamming codes, Hamming windows, Hamming numbers, and Hamming distance. In 1972, Nasir...

to a larger Hamming code. The adjective "transverse" is most often used when it is used in combination with additional error control coding, such as a...

Therefore, the minimum Hamming distance of the code equals its length n {\displaystyle n} . This gives the repetition code an error correcting capacity...

usually uses Hamming error correction. Some ECC memory uses triple modular redundancy hardware (rather than the more common Hamming code), because triple...

1/2). Richard Hamming Claude Shannon David J. C. MacKay Irving S. Reed Michael Luby Graph theory Hamming code Sparse graph code Expander code G.hn/G.9960...

error-correcting code works by including carefully crafted redundancy with the stored (or transmitted) data. Examples include Hamming codes, Reed–Solomon...

develop the 7-qubit code from the classical [7, 4] Hamming code, led to the construction of an important class of codes called the CSS codes, named for their...

modern development of error correction codes is credited to Richard Hamming in 1947. A description of Hamming's code appeared in Claude Shannon's A Mathematical...

(AMI) Coded mark inversion (CMI) EFMPlus, used in DVDs Eight-to-fourteen modulation (EFM), used in compact discs Hamming code Hybrid ternary code Manchester...

A binary code is called an even code if the Hamming weight of each of its codewords is even. An even code should have a generator polynomial that include...