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Upper bound in coding theory
theory, the Singleton bound, named after the American mathematician Richard Collom Singleton (1928–2007), is a relatively crude upper bound on the size
Singleton_bound
Family of error-correcting codes that encode data in blocks
\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
Block_code
Class of error-correcting 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
Linear_code
Topics referred to by the same term
theory Singleton pattern, a design pattern that allows only one instance of a class to exist Singleton bound, used in coding theory Singleton variable
Singleton
proof of the bound. Diamond code Elias Bassalygo bound Gilbert–Varshamov bound Griesmer bound Hamming bound Johnson bound Singleton bound Plotkin, Morris
Plotkin_bound
Error-correcting codes
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
Reed–Solomon_error_correction
Type of error-correcting codes
{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 }
Folded_Reed–Solomon_code
Coding theory concept
{\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
Zyablov_bound
omitted. Elias Bassalygo bound Gilbert-Varshamov bound Hamming bound Johnson bound Plotkin bound Singleton bound J. H. Griesmer, "A bound for error-correcting
Griesmer_bound
Limit on code size in coding theory
Elias-Bassalygo bound Gilbert–Varshamov bound for linear codes Griesmer bound Hamming bound Johnson bound Plotkin bound Singleton bound Gilbert, E. N. (1952), "A comparison
Gilbert–Varshamov_bound
Gilbert–Varshamov bound Griesmer bound Hamming bound Plotkin bound Singleton bound Johnson, Selmer Martin (April 1962). "A new upper bound for error-correcting
Johnson_bound
Limit on the parameters of a block code
packing radius. Gilbert-Varshamov bound Griesmer bound Johnson bound Plotkin bound Rate-distortion theory Singleton bound Tietäväinen 1973. McWilliams and
Hamming_bound
Represents a function with diffusion properties useful in cryptography
{\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
MDS_matrix
Type of block code
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
Cyclic_code
Signal coding technique
introduced by Gustave Solomon and J. J. Stiffler in 1964. Singleton bound, an upper bound in coding theory Chris Johnson. "Radio Access Networks for
Punctured_code
Regular graph with girth more than twice its diameter
_{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
Moore_graph
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
List of algebraic coding theory topics
List_of_algebraic_coding_theory_topics
code" of the Galileo space probe. Gilbert–Varshamov bound Justesen code Singleton bound Zyablov bound G. D. Forney (1967). "Concatenated codes". Cambridge
Concatenated error correction code
Concatenated_error_correction_code
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
Elias_Bassalygo_bound
Error-correcting code
{\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
Rank_error-correcting_code
Coding Theory
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
Locally_recoverable_code
Book
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
Introduction to the Theory of Error-Correcting Codes
Introduction_to_the_Theory_of_Error-Correcting_Codes
for membership in a set. singleton Pertains to an element that appears exactly once. In object-oriented programming, a singleton class has exactly one instance
Glossary_of_computer_science
Extremal graph problem with bounded degree and diameter
only known graphs attaining it are the Petersen graph and the Hoffman–Singleton graph; the only unresolved nontrivial parameter pair for equality is degree
Degree_diameter_problem
1st episode of the 2nd season of The Lowdown
Richard Robichaux as Lane Singleton Eddie Spears as Mekko Dean Episode chronology ← Previous "The Sensitive Kind" Next → "Whiskey Bent and Hell Bound"
The_Rupidoop
Cross-legged sitting meditation pose
Legend: Śrī-vikramaḥ (the courageous one). Mallinson & Singleton 2017, pp. 99–100. Mallinson & Singleton 2017, p. 111. Joshi, K. S. (1991). Yogic Pranayama:
Lotus_position
3rd episode of the 2nd season of The Lowdown
as Lonnie Reed Siena East as Deidra Richard Robichaux as Lane Singleton Episode chronology ← Previous "Whiskey Bent and Hell Bound" Next → "Raw Milk"
Truth's_Easy
Mathematical set containing no elements
York, NY: Pearson. ISBN 978-0134689517. A. Kanamori, "The Empty Set, the Singleton, and the Ordered Pair", p.275. Bulletin of Symbolic Logic vol. 9, no.
Empty_set
Spiritual practices from ancient India
Eliade 1958. Flood 1993, pp. 229ff. Jain 2016. Singleton 2010, pp. 32, 50. Singleton 2010, pp. 199–203. Singleton 2010, pp. 175–210. Sjoman 1999, pp. 39, 47
Yoga
Film directed by John Singleton
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
Abduction_(2011_film)
Public park in Boston, Massachusetts
neighborhood, bounded by Boylston Street, Clarendon Street, St. James Avenue, and Dartmouth Street. The square is named for painter John Singleton Copley. Prior
Copley_Square
American Television Series (1961-1966)
own plans to match Stan with a woman from his office, Mimi Lewis (Doris Singleton). George has Mimi over to meet Stan. Hazel invites Miss Lewis over under
List_of_Hazel_episodes
Generalization of compactness
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
Totally_bounded_space
All numbers between two given numbers
The intervals just described are the bounded intervals. Often intervals are also allowed to extend without bound in one or both directions, with the unbounded
Interval_(mathematics)
Collection of mathematical objects
is denoted ∅, ∅︀, or {}. A singleton is a set with exactly one element. If x is this element, the singleton is denoted {x}. The sets {∅︀}
Set_(mathematics)
Database operation
there is an upper bound to the number of results they will return. A query that returns exactly one result is sometimes called a singleton. Match at least
Range_query_(database)
Measure of algorithmic complexity
Turing's halting problem. In particular, no program P computing a lower bound for each text's Kolmogorov complexity can return a value essentially larger
Kolmogorov_complexity
Any one of the distinct objects that make up a set in set theory
relation ∋ {\displaystyle \ni } is a subset of P(U) × U. Identity element Singleton (mathematics) Weisstein, Eric W. "Element". mathworld.wolfram.com. Retrieved
Element_of_a_set
Brooks. Composer: Andy Razaf. Performer: Fats Waller. Orchestra: Zutty Singleton & His Orchestra. Stormy Weather (The Soundtrack Factory). The Soundtrack
List of Private Passions episodes (2020–present)
List_of_Private_Passions_episodes_(2020–present)
Mathematical-logic system
all functions from D to D has greater cardinality than D, unless D is a singleton set. In the 1970s, Dana Scott showed that if only continuous functions
Lambda_calculus
Infinite cardinal number
function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the extended real number line. ℵ 0 {\displaystyle
Aleph_number
American mathematician and computer scientist
lower bound for the problem given by a regular tree with the same degree. The graphs matching this bound were named Moore graphs by Hoffman & Singleton (1960)
Edward_F._Moore
Seated forward bending posture in hatha yoga
ISBN 978-81-7041-293-9. Mallinson, James (9 December 2011). "A Response to Mark Singleton's Yoga Body by James Mallinson". Retrieved 4 January 2019. revised from
Kurmasana
1994 software engineering book
class to create. Prototype creates objects by cloning an existing object. Singleton restricts object creation for a class to only one instance. Structural
Design_Patterns
Generalization of boundedness
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
Bounded set (topological vector space)
Bounded_set_(topological_vector_space)
Statement that is true regardless of the truth or falsity of its constituent propositions
power set identities Types of sets Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe
Logical_truth
Limitative results in mathematical logic
for any system that can represent enough arithmetic, there is an upper bound c such that no specific number can be proved in that system to have Kolmogorov
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Diagram that shows all possible logical relations between a collection of sets
Collectively exhaustive events Elementary event Mutual exclusivity Outcome Singleton Experiment Bernoulli trial Probability distribution Bernoulli distribution
Venn_diagram
Inequality applying to probability spaces
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
Boole's_inequality
largest possible graph for a given maximum degree and diameter. The Moore bound sets limits on this, but for many years mathematicians in the field have
Table of the largest known graphs of a given diameter and maximal degree
Table_of_the_largest_known_graphs_of_a_given_diameter_and_maximal_degree
Coastal plain in western Lancashire, England
Kirkham Lytham St Annes-on-the-Sea Wesham Elswick Freckleton Singleton Warton Weeton Wrea Green Blackpool Bispham Fleetwood Poulton-le-Fylde Thornton
The_Fylde
Probability distribution
and nk_=n(n−1)⋯(n−k+1) is the k-th falling power of n. A simple bound follows by bounding the Binomial moments via the higher Poisson moments:
Binomial_distribution
In first-order arithmetic, the induction principles, bounding principles, and least number principles are three related families of first-order principles
Induction, bounding and least number principles
Induction,_bounding_and_least_number_principles
English actress, comedian and writer (born 1972)
been diagnosed with Lyme disease, which led to her becoming bed and house-bound with ME/CFS. She has said "Probably when I was about 14 or 15, I got a tick-borne
Miranda_Hart
frigid weather in true Cajun fashion. Meanwhile, Frenchy Crochet and Gee Singleton see their best-laid plans literally blow up in their faces—threatening
List of Swamp People episodes (season 1–10)
List_of_Swamp_People_episodes_(season_1–10)
Little (1918) Lupe Vélez (1931) [citation needed] Chief Taby-Wana Joseph Singleton (1914) Noah Beery (1918) Mitchell Lewis (1931) Bloody Knife Stolen Women:
List of fictional Native Americans
List_of_fictional_Native_Americans
In logic, a statement which is always true
For instance, "If it's not bound, we know it's a book; if it's not bound, we know it's also not a book, so it is bound". ¬ ( A ∧ B ) ⇔ ( ¬ A ∨ ¬ B )
Tautology_(logic)
Theorem for proving more complex theorems
power set identities Types of sets Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe
Lemma_(mathematics)
Mandrell as Andrea, Juliet Mills as Kate Garfield, and Marti Stevens as Miss Singleton. 116 117 8 9 "Farnsworth's Fling" Richard Kinon Fred S. Fox & Seaman Jacobs
List of The Love Boat episodes
List_of_The_Love_Boat_episodes
American actress (born 1969)
playing Kristen Connor, a student discovering her sexuality, in John Singleton's Higher Learning. She also appeared in the film adaptation of the comic-book
Kristy_Swanson
Subpermutation of a longer permutation
which avoid all of the permutations in the set B. (In the case B is a singleton, say {β}, the abbreviation Avn(β) is used instead.) As noted above, MacMahon
Permutation_pattern
Concept in graph theory
complement of the aforementioned line graph on GQ(2, 4). The Hoffman–Singleton graph is an srg(50, 7, 0, 1). The Gewirtz graph is an srg(56, 10, 0, 2)
Strongly_regular_graph
Statement that is taken to be true
meaning that any nonempty set of real numbers with an upper bound has a least upper bound. However, expressing these properties as axioms requires the
Axiom
Somali-born American model and actress (born 1955)
Jackson short film and music video Remember the Time, directed by John Singleton. She portrayed the Queen of Ancient Egypt opposite Eddie Murphy as the
Iman_(model)
2021 sports drama film by Reinaldo Marcus Green
executive producers on the film), with Aunjanue Ellis, Saniyya Sidney, Demi Singleton, Tony Goldwyn, and Jon Bernthal in supporting roles. It premiered at the
King_Richard_(film)
Mathematical set formed from two given sets
elements of X. As a special case, the Cartesian 0th power of X is the singleton set, that has the empty function with codomain X as its unique element
Cartesian_product
(2003), Superman Returns (2006), X-Men: Days of Future Past (2014) John Singleton Tyrese Gibson Baby Boy (2001), 2 Fast 2 Furious (2003), Four Brothers
List of film director and actor collaborations
List_of_film_director_and_actor_collaborations
Mathematical ways to group elements of a set
is a partition of X, called the trivial partition. Particularly, every singleton set {x} has exactly one partition, namely { {x} }. For any non-empty proper
Partition_of_a_set
Mathematical proposition equivalent to the axiom of choice
most one maximal element. Upper bound Given a subset S of a partially ordered set P, an element u of P is an upper bound of S if it is greater than or equal
Zorn's_lemma
Discrete Fourier transform algorithm
Cambridge: Cambridge University Press. pp. 600–639. ISBN 978-0-521-88068-8. Singleton, R. (June 1969). "A short bibliography on the fast Fourier transform"
Fast_Fourier_transform
2024. McCaffrey, Lily (15 April 2024). "Ray Hadley confirmed to John Singleton that his daughter Dawn had been killed in Bondi Junction attack". news
2024_in_Australia
Set whose elements all belong to another set
power set identities Types of sets Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe
Subset
Impossible task in computing
power set identities Types of sets Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe
Entscheidungsproblem
List of postures in hatha yoga and yoga as exercise
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
List_of_asanas
Logical incompatibility between two or more propositions
power set identities Types of sets Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe
Contradiction
Branch of mathematics that studies sets
base subbase Ultrafilter Fuzzy Infinite (Dedekind-infinite) Recursive Singleton Subset · Superset Transitive Uncountable Universal Theories Alternative
Set_theory
5th 64% 35% Nilsa Cruz-Perez 6th 63% 35% James Beach 7th 64% 35% Troy Singleton 8th 50% 49% Latham Tiver 9th 35% 64% Carmen Amato 10th 35% 63% James W
2024 United States presidential election in New Jersey
2024_United_States_presidential_election_in_New_Jersey
Postures in hatha yoga and modern yoga practice
Mallinson & Singleton 2017, p. 108. Mallinson & Singleton 2017, pp. 108–111. Mallinson & Singleton 2017, pp. 359–361. Mallinson & Singleton 2017, pp. 385–387
Asana
3-volume treatise on mathematics, 1910–1913
precisely a version of it where the axiom of separation has all quantifiers bounded).[citation needed] The system of propositional logic and predicate calculus
Principia_Mathematica
2003 single by 702 featuring Pharrell
"Empire - Original Soundtrack". AllMusic. Retrieved September 18, 2023. Singleton, Mya (2022-11-05). "25 iconic songs produced by The Neptunes". Yardbarker
I_Still_Love_You_(702_song)
Peninsula located in Antarctica
northeast. To the south the Kvinge Peninsula is bounded by the Kauffman Glacier, which flows from Singleton Nunatak into Palmer Inlet. Palmer Inlet's mouth
Kvinge_Peninsula
Logical formulation of recursion
until a fixed point is reached. In implementations, it may be necessary to bound the number of iterations to limit the computation time. The resulting operators
Fixed-point_logic
American architect (1865–1924)
Louis Singleton Curtiss (July 1, 1865 – June 24, 1924) was a Canadian-born American architect. Notable as a pioneer of the curtain wall design, he was
Louis_Curtiss
Complexity class used to classify decision problems
in each step, and the length of the proof string must be polynomially bounded). If any proof is valid, some path will accept; if no proof is valid, the
NP_(complexity)
Set of the elements not in a given subset
base subbase Ultrafilter Fuzzy Infinite (Dedekind-infinite) Recursive Singleton Subset · Superset Transitive Uncountable Universal Theories Alternative
Complement_(set_theory)
and [□] for avoiding nested parentheses. 2. Set-builder notation for a singleton set: { x } {\displaystyle \{x\}} denotes the set that has x as a single
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Thick cold sauce
a rich and tangy taste that is commonly used on sandwiches, hamburgers, bound salads, and French fries. It also forms the base for other sauces, including
Mayonnaise
Set of elements common to all of some sets
The intersection of two geometric sets of points such as two lines is a singleton set of one point for distinct non-parallel lines in the same plane. We
Intersection_(set_theory)
for all rational c. By subadditivity, using the partition of 0:n−1 into singletons. g1≤g1g2≤g1+g1∘Tg3≤g1+g1∘T+g1∘T2⋯ Now, construct the sequence
Kingman's subadditive ergodic theorem
Kingman's_subadditive_ergodic_theorem
Mathematical operation with two operands
power set identities Types of sets Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe
Binary_operation
Type of logical system
then whether a variable occurrence is free or bound, then whether a variable symbol overall is free or bound. In order to distinguish different occurrences
First-order_logic
1978 film by Sidney Lumet
excuse to retreat to safer (i.e., whiter) creative ground until John Singleton and Spike Lee came along. Yet, without blaxploitation there might not
The_Wiz_(film)
Non-contradiction of a theory
power set identities Types of sets Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe
Consistency
South African sprinter and convicted murderer (born 1986)
slow start, he rallied to snatch gold from the United States' Jerome Singleton in the 100 metres in a time of 11.17 seconds, 0.03 seconds ahead of the
Oscar_Pistorius
1956 recording of Elvis Presley, Jerry Lee Lewis, Carl Perkins and Johnny Cash
time, Singleton licensed much, if not all, of the Sun catalogue to the British Charly label for reissue in Europe. As a result of Singleton's and Charly's
Million_Dollar_Quartet
Set of all things that may be the input of a mathematical function
power set identities Types of sets Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe
Domain_of_a_function
Australian science fiction author and mathematician
Crystal Nights (2008) Steve Fever (2007) TAP (1995) Induction (2007) Singleton (2002) Oracle (2000) Border Guards (1999) Hot Rock (2009) Oceanic (2009)
Greg_Egan
Symbol representing a property or relation in logic
replaced by a quantity interpreted as the degree of truth. Free variables and bound variables Hypostatic abstraction Multigrade predicate Opaque predicate Philosophical
Predicate_(logic)
Binary tree heap data structure
SkewHeap a = Empty | Node a (SkewHeap a) (SkewHeap a) singleton :: Ord a => a -> SkewHeap a singleton x = Node x Empty Empty union :: Ord a => SkewHeap a
Skew_heap
Paradox in set theory
base subbase Ultrafilter Fuzzy Infinite (Dedekind-infinite) Recursive Singleton Subset · Superset Transitive Uncountable Universal Theories Alternative
Russell's_paradox
travel, tourism, insurance
SINGLETON BOUND
SINGLETON BOUND
SINGLETON BOUND
SINGLETON BOUND
SINGLETON BOUND
SINGLETON BOUND
SINGLETON BOUND
SINGLETON BOUND
SINGLETON BOUND
travel, tourism, insurance