theory, the Singleton bound, named after the American mathematician Richard Collom Singleton (1928–2007), is a relatively crude upper bound on the size...

\cdot n-1} \over 2}\right\rfloor }{\binom {n}{i}}(q-1)^{i}\right]} The Singleton bound is that the sum of the rate and the relative distance of a block code...

e., having M code words), and minimum Hamming distance d.) Lemma (Singleton bound): Every linear [n,k,d] code C satisfies k + d ≤ n + 1 {\displaystyle...

theory Singleton pattern, a design pattern that allows only one instance of a class to exist Singleton bound, used in coding theory Singleton variable...

C(x) to produce c(x). The Singleton bound states that the minimum distance d of a linear block code of size (n,k) is upper-bounded by n - k + 1. The distance...

packing radius. Gilbert-Varshamov bound Griesmer bound Johnson bound Plotkin bound Rate-distortion theory Singleton bound Tietäväinen 1973. McWilliams and...

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

{k}{n}}} will be the same. According to the asymptotic version of the singleton bound, it is known that the relative distance δ {\displaystyle \delta } ...

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

Repetition code SEC-DED SFV SHA-1 SHA-2 Sanity testing Shaping codes Singleton bound Snake-in-the-box Snefru Soft output Viterbi algorithm Sparse graph...

introduced by Gustave Solomon and J. J. Stiffler in 1964. Singleton bound, an upper bound in coding theory Chris Johnson. "Radio Access Networks for...

{\displaystyle (x,f(x))} is an MDS code, i.e., a linear code that reaches the Singleton bound. Let A ~ = ( I n A ) {\displaystyle {\tilde {A}}={\begin{pmatrix}\mathrm...

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

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

{\displaystyle C_{in}} . Specifically, we suppose that the outer code meets the Singleton bound, i.e. it has rate r o u t {\displaystyle r_{out}} and relative distance...

code" of the Galileo space probe. Gilbert–Varshamov bound Justesen code Singleton bound Zyablov bound G. D. Forney (1967). "Concatenated codes". Cambridge...

check symbol. This property is also known as Rieger bound and it is similar to the Singleton bound for random error correcting. In 1959, Philip Fire presented...

_{i=0}^{k-1}(d-1)^{i}.} Hoffman & Singleton (1960) originally defined a Moore graph as a graph for which this bound on the number of vertices is met exactly...

1-H_{q}(J_{q}(\delta ))+o(1)} Gilbert–Varshamov bound Hamming bound Johnson bound Plotkin bound Singleton bound Each q {\displaystyle q} -ary block code of...

{\displaystyle d} . Such a linear rank metric code always satisfies the Singleton bound d ≤ n − k + 1 {\displaystyle d\leq n-k+1} with equality. There are...

Observe that we constructed an optimal LRC; therefore, using the Singleton bound, we have that the distance of this code is d = n − k − ⌈ k r ⌉ + 2...

metric is bounded but not totally bounded: every discrete ball of radius ε = 1 / 2 {\displaystyle \varepsilon =1/2} or less is a singleton, and no finite...

most d. The size of G is bounded above by the Moore bound; for 1 < k and 2 < d, only the Petersen graph, the Hoffman-Singleton graph, and possibly graphs...

and syndromes, sphere packing and the Hamming bound, the Singleton bound, and the Gilbert–Varshamov bound, and the Hamming(7,4) code. They also include...

Legend: Śrī-vikramaḥ (the courageous one). Mallinson & Singleton 2017, pp. 99–100. Mallinson & Singleton 2017, p. 111. Joshi, K. S. (1991). Yogic Pranayama:...

M)} : A lambda abstraction is a function definition, taking as input the bound variable x {\displaystyle x} (between the λ and the punctum/dot .) and returning...

subset is open in the discrete topology so that in particular, every singleton subset is an open set in the discrete topology. Given a set X {\displaystyle...

Abduction is a 2011 American action thriller film directed by John Singleton (in his final directed film before his death in 2019), produced by Roy Lee...

H(c):=\{h(c):h\in H\}} is a bounded subset of Y . {\displaystyle Y.} Since every singleton subset of X {\displaystyle X} is also a bounded subset, it follows that...

Mallinson & Singleton 2017, p. 108. Mallinson & Singleton 2017, pp. 108–111. Mallinson & Singleton 2017, pp. 359–361. Mallinson & Singleton 2017, pp. 385–387...