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...

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

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...

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...

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...

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...

transmits blocks containing n symbols. For example, the [7,4,3] Hamming code is a linear binary code which represents 4-bit messages using 7-bit codewords. Two...

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...

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

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

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;...

. 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...

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...

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...

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...

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...

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

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

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...

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

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...

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

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...

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...

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...

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

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

Conference: the IEEE CRC-32 polynomial is the generating polynomial of a Hamming code and was selected for its error detection performance. Even so, the Castagnoli...

(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...