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...

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

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...

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

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

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

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

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...

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...

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

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

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

\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...

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...

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

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...

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...

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)...

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...

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

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....

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...

-\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...

October 2003, Coppell was appointed manager of Reading, succeeding West Ham bound Alan Pardew (who had played under Coppell at Palace, in the late 1980s...

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...

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

{\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...

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...

including Hamming distance, decoding methods including maximum likelihood and syndromes, sphere packing and the Hamming bound, the Singleton bound, and the...