theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an...

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

Elias-Bassalygo bound Gilbert–Varshamov bound for linear codes Griesmer bound Hamming bound Johnson bound Plotkin bound Singleton bound Gilbert, E. N....

computer science and telecommunications, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors...

Sphere packing on the corners of a hypercube (with the spheres defined by Hamming distance) corresponds to designing error-correcting codes: if the spheres...

block codes. The first error-correcting code was the Hamming(7,4) code, developed by Richard W. Hamming in 1950. This code transforms a message consisting...

elements in an error-correcting code of a given block length and minimum Hamming weight over a field F q {\displaystyle \mathbb {F} _{q}} . This may be...

{\displaystyle \mathbb {F} _{q}} . Gilbert–Varshamov bound Griesmer bound Hamming bound Johnson bound Plotkin bound Keedwell, A. Donald; Dénes, József (24 January...

\rho n)|} be the volume of the Hamming ball of radius ρ n {\displaystyle \rho n} . It is obvious that the volume of a Hamming Ball is translation-invariant...

bound GOST (hash function) Group coded recording HAS-160 HAS-V HAVAL Hadamard code Hagelbarger code Hamming bound Hamming code Hamming(7,4) Hamming distance...

1+2C_{11}^{1}+2^{2}C_{11}^{2}=3^{5}} situations, i.e. the constructed WA lies on the Hamming bound for t = 2 {\displaystyle t=2} and in this sense is perfect. To date...

original on 2007-08-08. Retrieved 2007-08-21. Rudra, Atri. "Hamming code and Hamming bound" (PDF). Lecture notes. Rudolph, Dietmar; Rudolph, Matthias (2011-04-12)...

proof of the bound. Diamond code Elias Bassalygo bound Gilbert–Varshamov bound Griesmer bound Hamming bound Johnson bound Singleton bound Plotkin, Morris...

omitted. Elias Bassalygo bound Gilbert-Varshamov bound Hamming bound Johnson bound Plotkin bound Singleton bound J. H. Griesmer, "A bound for error-correcting...

Gilbert–Varshamov bound Griesmer bound Hamming bound Plotkin bound Singleton bound Johnson, Selmer Martin (April 1962). "A new upper bound for error-correcting...

In a cube In a cylinder Close-packing Kissing number Sphere-packing (Hamming) bound Other 2-D packing Square packing Other 3-D packing Tetrahedron Ellipsoid...

Gabriel graph Giant's Causeway Gradient pattern analysis Hamming bound – sphere-packing bound Linde–Buzo–Gray algorithm Lloyd's algorithm – Voronoi iteration...

communication" (PDF). U.S. patent no. 2,632,058 Morgan 1998, pp. 973–975. Hamming 1950, pp. 147–160. Ling & Xing 2004, pp. 82–88. Pless 1982, pp. 21–24....

Calderbank, Peter Shor and Andrew Steane. According to the quantum Hamming bound, encoding a single logical qubit and providing for arbitrary error correction...

2 {\displaystyle [2^{r}-1,2^{r}-r-1,3]_{2}} Hamming code. Since d = 3 {\displaystyle d=3} , this Hamming code can correct a 1-bit error. Example : The...

In communication complexity, the gap-Hamming problem asks, if Alice and Bob are each given a (potentially different) string, what is the minimal number...

{\bigl (}{\tfrac {n}{p}}+1{\bigr )}}}R^{n}.} n-sphere Sphere packing Hamming bound Equation 5.19.4, NIST Digital Library of Mathematical Functions. http://dlmf...

-\mathbf {x_{2}} )=0} . Since the minimum Hamming weight of ( 7 , 4 , 3 ) {\displaystyle (7,4,3)} Hamming Code is 3, d H ( x 1 , x 2 ) ≥ 3 {\displaystyle...

1996). "Class of quantum error-correcting codes saturating the quantum Hamming bound". Physical Review A. 54 (3): 1862–1868. arXiv:quant-ph/9604038. Bibcode:1996PhRvA...

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...

The Hamming(7,4) code may be written as a cyclic code over GF(2) with generator 1 + x + x 3 {\displaystyle 1+x+x^{3}} . In fact, any binary Hamming code...

Ham (in Hebrew: חָם), according to the Table of Nations in the Book of Genesis, was the second son of Noah and the father of Cush, Mizraim, Phut and Canaan...

salad): the primary ingredient, ham, is mixed with smaller amounts of chopped vegetables or relishes, and the whole is bound with liberal amounts of a mayonnaise...

fields, including communication complexity (e.g., in proofs of the gap Hamming problem) and graph theory. An interesting anti-concentration inequality...

the strings have the same size, the Hamming distance is an upper bound on the Levenshtein distance. The Hamming distance is the number of positions at...