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...

{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 } ...

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....

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

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

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

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...

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

{\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...

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...

{\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...

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...

_{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...

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...

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...

{\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...

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...

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...

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

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...

neighborhood, bounded by Boylston Street, Clarendon Street, St. James Avenue, and Dartmouth Street. The square is named for painter John Singleton Copley. Prior...

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...

who promoted Surya Namaskar". The Economic Times (India). Singleton 2010, pp. 199–203. Singleton 2010, pp. 175–210. Kest, Bryan (4 September 2017). "The...

with no elements, called the empty set; a set with a single element is a singleton. Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically...