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Study of the properties of codes and their fitness
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography
Coding_theory
Theory of cognition
Dual coding theory is a theory of cognition that suggests that the mind processes information along two different channels; verbal and nonverbal. It was
Dual-coding_theory
Type of error correcting code
and 5G New Radio (NR) Polar Coding with MATLAB®) and three appendices (Conceptual Channels in 5G New Radio, Channel Coding from 2G to 5G and Scripts),
Polar_code_(coding_theory)
Theory of brain function
Predictive coding is one member of a wider set of theories that follow the Bayesian brain hypothesis. Theoretical ancestors to predictive coding date back
Predictive_coding
Scientific study of digital information
Information theory has been used in a wide range of applications, such as source coding/data compression (e.g. for ZIP files), and channel coding/error detection
Information_theory
Limit on data transfer rate
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise
Noisy-channel_coding_theorem
Cognitive psychology theory
Common coding theory is a cognitive psychology theory describing how perceptual representations (e.g. of things we can see and hear) and motor representations
Common_coding_theory
Scheme for controlling errors in data over noisy communication channels
computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors
Error_correction_code
Canadian psychologist and writer (1925–2016)
representations: A dual coding approach. New York: Oxford University Press Clark, J.M., & Paivio, A. (1991). Dual coding theory and education. Educational
Allan_Paivio
Psychological phenomenon
pictures are coded more easily and can be retrieved from symbolic mode, while the dual coding process using words is more difficult for both coding and retrieval
Picture_superiority_effect
Topics referred to by the same term
programs Line coding, in data storage Source coding, compression used in data transmission Coding theory Channel coding Encryption coding, a process of
Coding
Branch of discrete mathematics
computational complexity theory. Coding theory started as a part of design theory with early combinatorial constructions of error-correcting codes. The main idea
Combinatorics
Establishes the limits to possible data compression
In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for
Shannon's source coding theorem
Shannon's_source_coding_theorem
Compact encoding of digital data
In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original
Data_compression
Subfield of computer science and mathematics
sub-fields of information theory are source coding, channel coding, algorithmic complexity theory, algorithmic information theory, information-theoretic
Theoretical_computer_science
Type of linear error-correcting code
page" in coding theory. There are two closely related binary Golay codes. The extended binary Golay code, G24 (sometimes just called the "Golay code" in finite
Binary_Golay_code
Code added to allow recovery of lost data
In coding theory, an erasure code is a forward error correction (FEC) code under the assumption of bit erasures (rather than bit errors), which transforms
Erasure_code
Study of computation
and on reliably storing and communicating data. Coding theory is the study of the properties of codes (systems for converting information from one form
Computer_science
Computer Networking Program
coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations. Linear network coding may
Linear_network_coding
Lossless data compression scheme
In information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared
Entropy_coding
Technique to compress data
symbols separately, Huffman coding is not always optimal among all compression methods – it is replaced with arithmetic coding if a better compression ratio
Huffman_coding
Data compression algorithms
Shannon–Fano coding should not be confused with Shannon–Fano–Elias coding (also known as Elias coding), the precursor to arithmetic coding. Regarding the
Shannon–Fano_coding
Linear error correcting code
turbo codes, they have gained prominence in coding theory and information theory since the late 1990s. The codes today are widely used in applications ranging
Low-density_parity-check_code
Type of code in coding theory
In coding theory, especially in telecommunications, a self-synchronizing code is a uniquely decodable code in which the symbol stream formed by a portion
Self-synchronizing_code
Cognitive and clinical psychology theory
Multiple code theory (MCT) is a theory that conceives of the human brain as processing information in three codes. A certain issue can be coded in three
Multiple_code_theory
Slepian and Jack Wolf discover and prove the Slepian–Wolf coding limits for distributed source coding 1976 – Gottfried Ungerboeck gives the first paper on
Timeline of information theory
Timeline_of_information_theory
Set of codewords, none a prefix of another
codes include Huffman codes and the earlier Shannon–Fano codes, and universal codes such as: Elias delta coding Elias gamma coding Elias omega coding
Prefix_code
Academic journal
van Lint, it is the leading research journal in the whole field of coding theory. A 2006 study using the PageRank network analysis algorithm found that
IEEE Transactions on Information Theory
IEEE_Transactions_on_Information_Theory
Binary Golay code Binary Goppa code Bipolar violation CRHF Casting out nines Check digit Chien's search Chipkill Cksum Coding gain Coding theory Constant-weight
List of algebraic coding theory topics
List_of_algebraic_coding_theory_topics
Number of bits that differ between two strings
mathematician Richard Hamming. A major application is in coding theory, more specifically to block codes, in which the equal-length strings are vectors over
Hamming_distance
Communication framework
Speech codes theory refers to a framework for communication in a given speech community. As an academic discipline, it explores the manner in which groups
Speech_codes_theory
Theoretical model of sensory neuroscience
optimized for coding images (or sounds) representative of those found in nature. Researchers have shown that filters optimized for coding natural images
Efficient_coding_hypothesis
Reliable digital data delivery methods on unreliable channels
In information theory and coding theory with applications in computer science and telecommunications, error detection and correction (EDAC) or error control
Error detection and correction
Error_detection_and_correction
System of rules to convert information into another form or representation
process, converting code symbols back into a form that the recipient understands, such as English, Spanish, etc. One reason for coding is to enable communication
Code
Study of discrete mathematical structures
computational topics. Information theory involves the quantification of information. Closely related is coding theory which is used to design efficient
Discrete_mathematics
In coding theory, the dual code of a linear code C ⊂ F q n {\displaystyle C\subset \mathbb {F} _{q}^{n}} is the linear code defined by C ⊥ = { x ∈ F q
Dual_code
Well-spaced set of points in a metric space
well-spaced they are. These sets have applications in coding theory, approximation algorithms, and the theory of quasicrystals. If (M, d) is a metric space,
Delone_set
Modulation scheme in telecommunication
Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. Inf. Theory, vol. IT-28, pp. 55–67, 1982. G. Ungerboeck, "Trellis-coded modulation with
Trellis_coded_modulation
English mathematician (1937–2020)
mathematician. He was active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions
John_Horton_Conway
Indian-born American computer scientist (1933–2024)
scientist recognized for foundational contributions to error-control coding, coding theory, and arithmetic processor reliability. A Fellow of both the Institute
T._R._N._Rao
Qualitative research methodology
after open coding, by making connections between categories." Glaser proposed a similar concept called theoretical coding. Theoretical codes help to develop
Grounded_theory
Family of linear error-correcting codes
error has occurred. Coding theory Gray code Golay code Hamming bound Hamming distance Low-density parity-check code Reed–Muller code Reed–Solomon error
Hamming_code
Error-correcting codes
In information theory and coding theory, Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon
Reed–Solomon_error_correction
Entropy encoding
. Although it is the optimal symbol-by-symbol coding for such probability distributions, Golomb coding achieves better compression capability for the
Unary_coding
Implicit representation of LGBT characters
identity. Queer coding may have had a negative impact on perceptions of queerness in media as villains are often queer-coded. Queer coding is a concept both
Queer_coding
Class of codes in coding theory
In coding theory, fountain codes (also known as rateless erasure codes) are a class of erasure codes with the property that a potentially limitless sequence
Fountain_code
notable unsolved problems in information theory. These are separated into source coding and channel coding. There are also related unsolved problems
List of unsolved problems in information theory
List_of_unsolved_problems_in_information_theory
Lossless data compression algorithm
contain repeats, where the entropy-coding cost of "spelling out" the repeats is less than the cost creating and entropy-coding a rule to capture them. (In general
Grammar-based_code
Simple but inefficient error-correcting code
In coding theory, the repetition code is one of the most basic linear error-correcting codes. In order to transmit a message over a noisy channel that
Repetition_code
Family of error-correcting codes that encode data in blocks
In coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks. There is a vast number of examples
Block_code
Theorem that tells the maximum rate at which information can be transmitted
noisy-channel coding theorem. This text also discusses state-of-the-art methods from coding theory, such as low-density parity-check codes, and Turbo codes. MIT
Shannon–Hartley_theorem
In statistics and coding theory, a Hamming space is usually the set of all 2 N {\displaystyle 2^{N}} binary strings of length N, where different binary
Hamming_space
American mathematician (1940–2019)
Block coding with noiseless feedback. Thesis, Massachusetts Institute of Technology, Dept. of Electrical Engineering, 1964. Algebraic Coding Theory, New
Elwyn_Berlekamp
Mathematician, programmer
of coding theory, and was one of the first women to publish in the field. MacWilliams' thesis "Combinatorial Problems of Elementary Group Theory" (or
Jessie_MacWilliams
Signal coding technique
In coding theory, puncturing is the process of removing some of the parity bits after encoding with an error-correction code. This has the same effect
Punctured_code
Theory of subatomic structure
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called
String_theory
Mathematical linear code
Goppa codes are a distinct class of codes which were also constructed by Goppa in the early 1970s. These codes attracted interest in the coding theory community
Algebraic_geometry_code
coding: adaptive coding technique based on Huffman coding Package-merge algorithm: Optimizes Huffman coding subject to a length restriction on code strings
List_of_algorithms
Topics referred to by the same term
Diamond code may refer to: Diamond code (genetics), a (wrong) proposal by George Gamow how to denote DNA sequences Diamond code (coding theory), a self-complementing
Diamond_code
Common communications channel model
(or BSCp) is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit (a zero
Binary_symmetric_channel
Encoding which maps information to a variable number of bits
In coding theory, variable-length encoding is a type of character encoding scheme in which codes of differing lengths are used to encode a character set
Variable-length_encoding
In coding theory, telecommunications engineering and other related engineering problems, coding gain is the measure in the difference between the signal-to-noise
Coding_gain
Russian mathematician (1935–2017)
systematic codes", Doklady Akademii Nauk SSSR, 131 (5): 1011–1014 V.I. Levenshtein, Application of Hadamard matrices to a problem in coding theory, Problems
Vladimir_Levenshtein
American mathematician (1932–2016)
1953. He specialized in problems of combinatorial analysis, number theory, coding theory, and communications. Pentomino board games, based on his work, would
Solomon_W._Golomb
Algebraic structure with addition, multiplication, and division
equation of the form y2 = x3 + ax + b. Finite fields are also used in coding theory and combinatorics. Functions on a suitable topological space X into
Field_(mathematics)
theory Coding theory Cohomology theory Theory of Computation Continuum theory Control theory Deformation theory Dempster–Shafer theory Dimension theory Distribution
List_of_mathematical_theories
Physical theory with fields invariant under the action of local "gauge" Lie groups
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local
Gauge_theory
Theory in statistics
significance in classical coding theory. In coding theory, association scheme theory is mainly concerned with the distance of a code. The linear programming
Association_scheme
Method for encoding data in communications
In coding theory, a constant-weight code, also called an m-of-n code or m-out-of-n code, is an error detection and correction code where all codewords
Constant-weight_code
Error correction code
In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials
BCH_code
Type of data compression
AAC). In the case of audio data, a popular form of transform coding is perceptual coding, which transforms the raw data to a domain that more accurately
Lossy_compression
Abstraction of linear independence of vectors
applications in geometry, topology, combinatorial optimization, network theory, and coding theory. There are many equivalent ways to define a (finite) matroid.
Matroid
Topics referred to by the same term
recorded in a sample Inner distribution, and outer distribution, in coding theory Distributed parameter system, systems that have an infinite-dimensional
Distribution
Type of block code
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting
Cyclic_code
Set of "near" codewords in coding theory
In coding theory, a covering code is a set of elements (called codewords) in a space, with the property that every element of the space is within a fixed
Covering_code
Coding tree unit (CTU) is the basic processing unit of the High Efficiency Video Coding (HEVC) video standard and conceptually corresponds in structure
Coding_tree_unit
Australian mathematician
an Australian mathematician who works in group theory, combinatorics, coding theory, and model theory. He is currently Emeritus Professor at the University
Peter_Cameron_(mathematician)
Class of error-correcting code
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally
Linear_code
Bipartite graph in coding theory
In coding theory, a Tanner graph is a bipartite graph that can be used to express constraints (typically equations) that specify an error correcting code
Tanner_graph
Collection of random variables
In probability theory and related fields a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random variables
Stochastic_process
Sequence of digital values used for synchronisation
17th International Conference Radioelektronikachapter = CCK and Barker Coding Implementation in IEEE 802.11b Standard. pp. 1–4. doi:10.1109/RADIOELEK
Barker_code
American mathematician
Dean of Natural Sciences. His contributions to coding and information theory won the IEEE Information Theory Society Paper Award in 1995 and 1999. He was
Robert_Calderbank
Method by which information is represented in the brain
or "spike firing", increases. Rate coding is sometimes called frequency coding. Rate coding is a traditional coding scheme, assuming that most, if not
Neural_coding
American mathematician (born 1957)
Lander studied combinatorics and applications of representation theory to coding theory. He enjoyed mathematics but did not wish to spend his life in such
Eric_Lander
Concept in coding theory
In coding theory, the Kraft–McMillan inequality gives a necessary and sufficient condition for the existence of a prefix code (in Leon G. Kraft's version)
Kraft–McMillan_inequality
American mathematician
information theory, and coding theory. In coding theory he proved the Interactive Coding Theorem (a generalization of the Shannon Coding Theorem.) In
Leonard_Schulman
Methods of mathematical approximation
In mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related
Perturbation_theory
Algebraic structure
computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. A finite field is a field that
Finite_field
Mathematical approach to quantum physics
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Branch of mathematics concerning probability
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations
Probability_theory
Limit on the parameters of a block code
computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing
Hamming_bound
Supposition or system of ideas intended to explain something
Approximation theory — Arakelov theory — Asymptotic theory — Bifurcation theory — Catastrophe theory — Category theory — Chaos theory — Choquet theory — Coding theory
Theory
author) Papers by Petar Maymounkov A Ruby project hosted at RubyForge containing a Ruby library for Online Coding Archived 2016-03-03 at the Wayback Machine
Online_codes
Concept in coding theory
In coding theory, triangular network coding (TNC) is a non-linear network coding based packet coding scheme introduced by Qureshi, Foh & Cai (2012). Previously
Triangular_network_coding
Error-correcting code
Hadamard code is not only used by engineers, but also intensely studied in coding theory, mathematics, and theoretical computer science. The Hadamard code is
Hadamard_code
Form of entropy encoding used in data compression
Arithmetic coding (AC) is a form of entropy coding used in lossless data compression. Normally, a string of characters is represented using a fixed number
Arithmetic_coding
Concept in coding theory
In coding theory, a zigzag code is a type of linear error-correcting code introduced by Ping, Huang & Phamdo (2001). They are defined by partitioning the
Zigzag_code
Part of coding theory
In coding theory, a parity-check matrix of a linear block code C is a matrix which describes the linear relations that the components of a codeword must
Parity-check_matrix
Matrix generating a linear code
In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code. The codewords are all of the linear combinations of the rows
Generator_matrix
American electrical engineer (born 1940)
made contributions in telecommunication system theory, specifically in coding theory and information theory. Forney received the B.S.E. degree in electrical
Dave_Forney
CODING THEORY
CODING THEORY
Boy/Male
Indian
Loving, Caring, Daring
Boy/Male
Arabic, Muslim, Pashtun
Loving and Caring
Surname or Lastname
English
English : from the Old Norse personal name Kollungr, a derivative of Koli, or from an Old English cognate, Colling, a derivative of Cola (see Cole 2).English : from a pet form of Coll 1.Altered spelling of German Kölling (see Kolling).
Surname or Lastname
English
English : variant of Colling.
Girl/Female
Bengali, Gujarati, Hindu, Indian, Japanese
Sweet; Loving and Caring; Pretty
Boy/Male
Muslim
Loving, Caring, Daring
Girl/Female
Arabic, Muslim
Caring; Loving
Female
Scottish
Scottish feminine form of English Rodney, RODINA means "Hroda's fen/island."
Surname or Lastname
English
English : from a medieval personal name, originally an Old English patronymic from the personal names Cūl(a) or Cēola. The former may be from a Germanic root kūl ‘swollen’; the latter is a short form of various compound names with the first element cēol ‘ship’.English : habitational name from a place in Kent named Cooling, from the Old English tribal name Cūlingas ‘people of Cūl(a)’.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : from a double diminutive of Codd.English (Yorkshire) : from Old French ceur de lion ‘lion heart’, applied as a nickname for a brave man, or ironically for an exceptionally timorous one.
Surname or Lastname
English
English : habitational name from places in Oxfordshire and West Sussex named Goring, from Old English GÄringas ‘people of GÄra’, a short form of the various compound names with the first element gÄr ‘spear’.German (Göring) : see Goering.
Girl/Female
Arabic, Indian, Muslim
Caring; Loving
Surname or Lastname
English
English : variant of Gooding.German (Göding) : variant of Godding.
Female
French
Variant spelling of French Corinne, CORINE means "maiden."
Female
English
Variant spelling of English Colleen, COLINE means "girl."
Surname or Lastname
English (Somerset)
English (Somerset) : unexplained.
Girl/Female
Arabic, Australian
Enchanting; Kind; Loving; Caring
Surname or Lastname
Danish
Danish : probably a habitational name from Kolding. This was originally the name of a river, from kaldr ‘cold’ + a derivational suffix -ung, hence ‘the cold river’.English : perhaps a spelling variant of Golding.
Boy/Male
Muslim/Islamic
Loving Caring, Daring
Surname or Lastname
English
English : from the late Old English personal name Golding, in form a patronymic from Golda (see Gold 4).German : patronymic from a short form of a Germanic personal name formed with gold, guld ‘gold’, ‘bright’.Jewish (from Latvia and Lithuania) : habitational name from Golding, the German and Yiddish name of the city of Kuldīga in Latvia.
CODING THEORY
CODING THEORY
Male
Hebrew
(×’Ö¼Ö´× Ö¼Ö¸×”) Hebrew unisex name GINA means "garden." Compare with strictly feminine forms of Gina.
Girl/Female
Hindu, Indian
Capable
Girl/Female
Indian, Latin, Traditional
Life
Boy/Male
Hindu, Indian, Punjabi, Sikh
The Blessed One
Boy/Male
Indian, Tamil
Youthful and Brilliant
Biblical
desiring God
Boy/Male
Hindu
A flower
Boy/Male
Armenian, Gujarati, Hindu, Indian, Muslim, Punjabi, Sikh
Powerful
Surname or Lastname
English
English : variant spelling of Revell.
Boy/Male
Tamil
Unique
CODING THEORY
CODING THEORY
CODING THEORY
CODING THEORY
CODING THEORY
a.
Approaching; of the future, especially the near future; the next; as, the coming week or year; the coming exhibition.
n.
The chips or fragments made by boring.
n.
A prognostic; an omen; a foreboding.
p. pr. & vb. n.
of Cede
a.
Boding evil; inauspicious; ill-omened.
p. pr. & vb. n.
of Bode
a.
Ever closing.
n.
Alt. of Codling
n.
A hole made by boring.
n.
Any boxlike inclosure or recess; a casing.
n.
Coming.
a.
The act or process of preparing staple for spinning, etc., by carding it. See the Note under Card, v. t.
p. pr. & vb. n.
of Coy
p. pr. & vb. n.
of Cow
n.
Approach; advent; manifestation; as, the coming of the train.
v. t.
A roll of wool or other fiber as it comes from the carding machine.
n.
The act or process of one who, or that which, bores; as, the boring of cannon; the boring of piles and ship timbers by certain marine mollusks.
n.
A coat or covering; a layer of any substance, as a cover or protection; as, the coating of a retort or vial.
n.
A stone for coping. See Coping.
a.
Foreshowing; presaging; ominous.