In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code C...

\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...

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

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...

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

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

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...

{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 } ...

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...

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...

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...

{\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...

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

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 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...

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

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

_{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...

In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at...

{\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...

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

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...

positive or negative infinity, indicating the interval extends without a bound. A real interval can contain neither endpoint, either endpoint, or both...

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...

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

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...

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

Mallinson & Singleton 2017, p. xxxix. Powers 2008, p. 195. Mehta, Mehta & Mehta 1990, p. 147. Singleton 2010, pp. 205–206. Mallinson & Singleton 2017, p. 125...

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