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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
Optical machine-readable representation of data
other patterns, called matrix codes or 2D barcodes. Despite being often included as barcodes, these do not use bars as linear barcodes do. These can be read
Barcode
Digital representation of sampled analog signals
patent granted in 1952. Linear pulse-code modulation (LPCM) is a specific type of PCM in which the quantization levels are linearly uniform. This is in contrast
Pulse-code_modulation
Computer Networking Program
linear network coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations. Linear network
Linear_network_coding
The Gilbert–Varshamov bound for linear codes is related to the general Gilbert–Varshamov bound, which gives a lower bound on the maximal number of elements
Gilbert–Varshamov bound for linear codes
Gilbert–Varshamov_bound_for_linear_codes
Speech analysis and encoding technique
Linear predictive coding (LPC) is a method used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital
Linear_predictive_coding
Software analysis method to identify structural units in code
Linear code sequence and jump (LCSAJ), in the broad sense, is a software analysis method used to identify structural units in code under test. Its primary
Linear_code_sequence_and_jump
Speech coding algorithm
Code-excited linear prediction (CELP) is a linear predictive speech coding algorithm originally proposed by Manfred R. Schroeder and Bishnu S. Atal in
Code-excited linear prediction
Code-excited_linear_prediction
Study of the properties of codes and their fitness
the code. There are many types of linear block codes, such as Cyclic codes (e.g., Hamming codes) Repetition codes Parity codes Polynomial codes (e.g
Coding_theory
Family of linear error-correcting codes
computer science and telecommunications, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or
Hamming_code
Error-correcting code
involved, and is described under Constructions. It is an example of a linear code of length 2 m {\displaystyle 2^{m}} over a binary alphabet. Unfortunately
Hadamard_code
Cryptography secured against quantum computers
proposed a random linear code encryption scheme RLCE which is based on McEliece schemes. A RLCE scheme can be constructed using any linear code such as Reed-Solomon
Post-quantum_cryptography
Family of error-correcting codes that encode data in blocks
codes, Hadamard codes, Expander codes, Golay codes, Reed–Muller codes and Polar codes. These examples also belong to the class of linear codes, and hence they
Block_code
Syllabic script used for writing Mycenaean Greek
contains Linear B Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Linear B. Linear B is
Linear_B
Metric for source code testing
PVC. There are further coverage criteria, which are used less often: Linear Code Sequence and Jump (LCSAJ) coverage a.k.a. JJ-Path coverage – has every
Code_coverage
Type of linear error-correcting code
Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has deep
Binary_Golay_code
Pair of related error-correcting codes
-code, that is, it is a linear code over a ternary alphabet; the relative distance of the code is as large as it possibly can be for a ternary code, and
Ternary_Golay_code
Speech coding standard
Algebraic code-excited linear prediction (ACELP) is a speech coding algorithm in which a limited set of pulses is distributed as excitation to a linear prediction
Algebraic code-excited linear prediction
Algebraic_code-excited_linear_prediction
Type of linear code
In coding theory, a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length)
Polynomial_code
Undeciphered writing system of ancient Crete
contains Linear A Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Linear A. Linear A is
Linear_A
Linear error correcting code
Institute of Technology. The codes were largely ignored at the time, as their iterative decoding algorithm (despite having linear complexity) was prohibitively
Low-density_parity-check_code
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
Error-correcting code
In coding theory, rank codes (also called Gabidulin codes) are non-binary linear error-correcting codes over not Hamming but rank metric. They described
Rank_error-correcting_code
Mathematical linear code
Algebraic geometry codes, often abbreviated AG codes, are a type of linear code that generalize Reed–Solomon codes. The Russian mathematician V. D. Goppa
Algebraic_geometry_code
Scheme for controlling errors in data over noisy communication channels
code Linear Network Coding, a type of erasure correcting code across networks instead of point-to-point links Long code Low-density parity-check code
Error_correction_code
Upper bound in coding theory
(1953). Linear block codes that achieve equality in the Singleton bound are called MDS (maximum distance separable) codes. Examples of such codes include
Singleton_bound
Error-correcting codes
&g_{k,n}\end{bmatrix}}} The Reed–Solomon code is a [n, k, n − k + 1] code; in other words, it is a linear block code of length n (over F) with dimension k
Reed–Solomon_error_correction
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
Limit on code size in coding theory
coding theory, the Gilbert–Varshamov bound (due to Edgar Gilbert and independently Rom Varshamov) is a bound on the size of a (not necessarily linear)
Gilbert–Varshamov_bound
Coding Theory
[n,k,d,r]_{q}} LRC is an [ n , k , d ] q {\displaystyle [n,k,d]_{q}} linear code such that there is a function f i {\displaystyle f_{i}} that takes as
Locally_recoverable_code
Systematic naming of carbohydrate-based polymers
{[(3+1)][A-D-MANP]{}[(6+1)][A-D-MANP]{}}}[(6+1)][A-L-FUCP]{}}} Linear Code is a linear notation proposed by GlycoMinds Ltd. and is one of the most compact
Glycan_nomenclature
remote site at a later time. Every non-systematic linear code can be transformed into a systematic code with essentially the same properties (i.e., minimum
Systematic_code
Class of quantum error correcting codes
linear codes with some special properties. Examples of CSS codes include the Shor code, Steane code, the toric code, and more general surface codes.
CSS_code
Type of block code
{\displaystyle n-1} cyclic left shifts, a cyclic code may also be defined via cyclic left shifts. Therefore, the linear code C {\displaystyle {\mathcal {C}}} is cyclic
Cyclic_code
Class of codes in coding theory
LT codes were the first practical realization of fountain codes. Raptor codes and online codes were subsequently introduced, and achieve linear time
Fountain_code
Speech codec by Qualcomm
Qualcomm code-excited linear prediction (QCELP), also known as Qualcomm PureVoice, is a speech codec developed in 1994 by Qualcomm to increase the speech
Qualcomm code-excited linear prediction
Qualcomm_code-excited_linear_prediction
Specifies the number of words of a binary linear code of each possible Hamming weight
In coding theory, the weight enumerator polynomial of a binary linear code specifies the number of words of each possible Hamming weight. Let C ⊂ F 2
Enumerator_polynomial
Asymmetric encryption algorithm developed by Robert McEliece
from the private key by disguising the selected code as a general linear code. For this, the code's generator matrix G {\displaystyle G} is perturbated
McEliece_cryptosystem
Bipartite graph in coding theory
following bounds Let R {\displaystyle R} be the rate of the resulting linear code, let the degree of the digit nodes be m {\displaystyle m} and the degree
Tanner_graph
code of length N; the elements of C are called codewords. In the case where C is a linear subspace of its Hamming space, it is called a linear code.
Hamming_space
Decoding method
information theory and coding theory, linear programming decoding (LP decoding) is a decoding method which uses concepts from linear programming (LP) theory
Linear_programming_decoding
Audio codec standard
Relaxed code-excited linear prediction (RCELP) is a method used in some advanced speech codecs. The RCELP algorithm does not attempt to match the original
Relaxed code-excited linear prediction
Relaxed_code-excited_linear_prediction
Neil Sloane. The binary lexicographic codes are linear codes, and include the Hamming codes and the binary Golay codes. A lexicode of length n and minimum
Lexicographic_code
Problem in information theory and communication
linear codes, they have translated the major steps of DSC joint decoding into syndrome decoding followed by channel encoding via a linear block code and
Distributed_source_coding
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
Code sequence with no branches except at entry and exit
(programming) Control-flow graph Decision-to-decision path Extended basic block Linear code sequence and jump Hennessy, John L.; David A. Patterson. Computer architecture:
Basic_block
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
Mathematical function, in linear algebra
In mathematics, and more specifically in linear algebra, a linear map (or linear mapping) is a particular kind of function between vector spaces, which
Linear_map
Algorithms to decode messages
This is allowed by the linearity of the code. Suppose that C ⊂ F 2 n {\displaystyle C\subset \mathbb {F} _{2}^{n}} is a linear code of length n {\displaystyle
Decoding_methods
Natural number
number 24 also occurs in coding theory and finite group theory through the extended binary Golay code, a self-dual binary linear code with parameters [ 24
24_(number)
Method to solve optimization problems
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical
Linear_programming
Error-correcting code
the expense of an alphabet size that is linear in the message length. The Wozencraft ensemble is a family of codes that achieve constant rate and constant
Justesen_code
Coding theory algorithm
codes, where the underlying graph is bipartite graph. Sipser and Spielman introduced a constructive family of asymptotically good linear-error codes together
Zemor's_decoding_algorithm
Linear predictive coding
Warped linear predictive coding (warped LPC or WLPC) is a variant of linear predictive coding in which the spectral representation of the system is modified
Warped linear predictive coding
Warped_linear_predictive_coding
Type of shift register in computing
linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function
Linear-feedback shift register
Linear-feedback_shift_register
Sudoku codes are non-linear forward error correcting codes following rules of sudoku puzzles designed for an erasure channel. Based on this model, the
Sudoku_code
A Sparse graph code is a code which is represented by a sparse graph. Any linear code can be represented as a graph, where there are two sets of nodes
Sparse_graph_code
Codes intended to correct short, contiguous errors in a communications channel
k ) {\displaystyle (n,k)} linear block code, then 2 ℓ ⩽ n − k {\displaystyle 2\ell \leqslant n-k} . Proof Any linear code that can correct any burst
Burst_error-correcting_code
Error-correcting codes used in wireless communication
channels. Reed–Muller codes generalize the Reed–Solomon codes and the Walsh–Hadamard code. Reed–Muller codes are linear block codes that are locally testable
Reed–Muller_code
Array for a particular vector space
are used to decode linear codes; i.e. to find the corresponding codeword for any received vector. A standard array for an [n,k]-code is a q n − k {\displaystyle
Standard_array
Linear feedforward neural network model
\mathbb {R} ^{n}} , and can be (approximately) represented as a linear sum of linear code vectors w 1 , … , w m ∈ R n {\displaystyle w_{1},\dots ,w_{m}\in
Generalized_Hebbian_algorithm
Timecode encoded as an audio signal
Linear (or Longitudinal) Timecode (LTC) is an encoding of SMPTE timecode data in an audio signal, as defined in SMPTE 12M specification. The audio signal
Linear_timecode
Ordering of binary values, used for positioning and error correction
also called modified Gray code De Bruijn sequence Hamming code Hilbert curve Linear-feedback shift register Minimum distance code Prouhet–Thue–Morse sequence
Gray_code
Type of two-dimensional barcode
A QR code, short for quick-response code, is a type of two-dimensional matrix barcode invented in 1994 by Masahiro Hara of the Japanese company Denso
QR_code
Class of error correction codes
k , d ] q {\displaystyle [n,k,d]_{q}} linear block code, one can prove that there exists a permutation code in the symmetric group of degree n {\displaystyle
Permutation_code
Topics referred to by the same term
a data structure in computer science Ternary Golay code, a perfect [11, 6, 5] ternary linear code ?:, a ternary conditional operator used for basic conditional
Ternary
If the Hamming weight of all of a binary code's codewords is even
A binary linear code is called an even code if the Hamming weight of each of its codewords is even. An even code should have a generator polynomial that
Even_code
Converting computer code into a machine readable form
The input to the code generator typically consists of a parse tree or an abstract syntax tree. The tree is converted into a linear sequence of instructions
Code_generation_(compiler)
In coding theory, the Wozencraft ensemble is a set of linear codes in which most of codes satisfy the Gilbert-Varshamov bound. It is named after John Wozencraft
Wozencraft_ensemble
Barcode format
Code 128 is a high-density linear barcode symbology defined in ISO/IEC 15417:2007. It is used for alphanumeric or numeric-only barcodes. It can encode
Code_128
Topics referred to by the same term
up linear in Wiktionary, the free dictionary. Linearity is a property of various things in mathematics, physics, and electronics. Linear, linearly, or
Linear_(disambiguation)
In coding theory, the Preparata codes form a class of non-linear double-error-correcting codes. They are named after Franco P. Preparata who first described
Preparata_code
Linear error-correcting code
In coding theory, Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member
Hamming(7,4)
Type of error correcting code
polar codes are a linear block error-correcting codes. The code construction is based on a multiple recursive concatenation of a short kernel code which
Polar_code_(coding_theory)
Represents a function with diffusion properties useful in cryptography
(m+n)} -tuples ( x , f ( x ) ) {\displaystyle (x,f(x))} is an MDS code, i.e., a linear code that reaches the Singleton bound. Let A ~ = ( I n A ) {\displaystyle
MDS_matrix
the mathematics of coding theory, the Griesmer bound, named after James Hugo Griesmer, is a bound on the length of linear binary codes of dimension k and
Griesmer_bound
block length of the code. In coding theory, an expander code is a [ n , n − m ] 2 {\displaystyle [n,n-m]_{2}\,} linear block code whose parity check matrix
Expander_code
Classification of algorithm
performance was much better than other codes of that time, reaching the Gilbert–Varshamov bound for linear codes, the codes were largely ignored as their iterative
Galactic_algorithm
Delsarte–Goethals code was published in 1970. The Delsarte–Goethals code DG(m,r) for even m ≥ 4 and 0 ≤ r ≤ m/2 − 1 is a binary, non-linear code of length 2
Delsarte–Goethals_code
Memory debugger software
occurred. Additionally, Insure++ will produce Linear Code Sequence and Jump Code Coverage metrics for all tested code. Runtime error detection Software development
Insure++
Computer science professor
research, he is known for the invention of the quantum resistant random linear code based encryption scheme RLCE. "IEEE P1363.2 Draft Download". IEEE. Archived
Yongge_Wang
Common communications channel model
C in {\displaystyle C_{\text{in}}} we find a linear code by exhaustively searching from the linear code of block length n {\displaystyle n} and dimension
Binary_symmetric_channel
Type of matrix factorization
In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix
LU_decomposition
ITU-T recommendation
sequence of repeating code values which defines the power level of 0 dB. The μ-law and A-law algorithms encode 14-bit and 13-bit signed linear PCM samples (respectively)
G.711
Cryptographic algorithm created by Adi Shamir
Villar, José L. (2009). "On proper secrets, (t,k)-bases and linear codes". Designs, Codes and Cryptography. 52 (2): 129–154. doi:10.1007/s10623-009-9272-4
Shamir's_secret_sharing
Technique to compress data
symbols. Huffman's method can be efficiently implemented, finding a code in time linear to the number of input weights if these weights are sorted. However
Huffman_coding
Type of barcode
ISO 15438. The PDF417 bar code (also called a symbol) consists of 3 to 90 rows, each of which is like a small linear bar code. Each row has: A quiet zone
PDF417
Index of articles associated with the same name
Cyclic chain rule, for derivatives, used in thermodynamics Cyclic code, linear codes closed under cyclic permutations Cyclic convolution, a method of combining
Cyclic_(mathematics)
achievable by concatenated codes. The bound states that there exists a family of q {\displaystyle q} -ary (concatenated, linear) codes with rate r {\displaystyle
Zyablov_bound
British computer scientist (born 1940)
in the use of Static code analysis for quantifying the effectiveness of test data, which led to the development of the Linear Code Sequence and Jump concept
Michael_Hennell
Mathematical game
game can be used in coding theory as a demonstration of the covering radius of a certain binary linear code. A binary linear code of length n {\displaystyle
Berlekamp_switching_game
Niederreiter. It applies the same idea to the parity check matrix, H, of a linear code. Niederreiter is equivalent to McEliece from a security point of view
Niederreiter_cryptosystem
In coding theory, the hexacode is a length 6 linear code of dimension 3 over the Galois field G F ( 4 ) = { 0 , 1 , ω , ω 2 } {\displaystyle GF(4)=\{0
Hexacode
Routines for performing common linear algebra operations
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations
Basic Linear Algebra Subprograms
Basic_Linear_Algebra_Subprograms
Software library for numerical linear algebra
LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations
LAPACK
Path of execution between decisions
(2013), in Great Britain and ISTQB literature, the same notion is called linear code sequence and jump (LCSAJ).[dubious – discuss] From the latter definition
Decision-to-decision_path
Cryptographic primitives that involve lattices
Regev, Oded (2005-01-01). "On lattices, learning with errors, random linear codes, and cryptography". Proceedings of the thirty-seventh annual ACM symposium
Lattice-based_cryptography
American information theorist, cryptographer, and scholar (1934 – 2013)
notable work includes the application of the Berlekamp–Massey algorithm to linear codes, the design of the block ciphers IDEA (with Xuejia Lai, based on the
James_Massey
Mathematical operation that predicts future values of a discrete-time signal
previous samples. In digital signal processing, linear prediction is often called linear predictive coding (LPC) and can thus be viewed as a subset of filter
Linear_prediction
ℓ+1 code, which is a linear code. Since every BCH code can be presented as a polynomial-time computable restriction of a related Reed Solomon code, which
MAXEkSAT
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