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Everything about Linear code
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 partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types. Linear codes allow for more efficient encoding and decoding algorithms than other codes. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Linear codeA 5-minute orientation
- Skim a recent paper: Neural Belief Propagation Auto-Encoder for Linear Block Code DesignInfluential work since 2022
- Pick up a classic book: Some modern applications of mathematicsThe most-reprinted book on the subject
- Read the landmark paper: Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)Cited 4,888 times
- Go sideways: Singleton boundA closely related topic
- Go sideways: Decoding methodsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)
Frequency-hopping code sequence designs having large linear span
Detection and recognition of a binary linear code
A Novel Linear Code Nomenclature for Complex Carbohydrates.
Linear binary code for write-once memories (Corresp.)
SPORTS - A simple non-linear thermalhydraulic stability code
PCx: an interior-point code for linear programming
LPNORM: A linear programming normative analysis code
🆕 Influential since 2022
Neural Belief Propagation Auto-Encoder for Linear Block Code Design
Cheers: A Linear‐Scaling KBE + GKBA Code
NC92Soil: A computer code for deterministic and stochastic 1D equivalent linear seismic site response analyses
Linear Precoding for Space-Time Line Code-Based Multicast Systems
Spreading Code Estimation Using Inherent Linear Relation in Non-Cooperative Contexts
📚 Books worth reading
Some modern applications of mathematicsStephen Barnett · 1995- 📕On complexity of trellis structure of linear block codesLin, Shu. · 1990
- 📕L P B L K DAndré F. Perold · 1979
- 📕The binary weight distribution of the extended (2[superscript m], 2[superscript m]-4) code of Reed-Solomon code over GF(2[superscript m]) with generator polynomial (x-[alpha])(x-[alpha]²)(x-[alpha]³)Shu Lin · 1987
- 📕Generalized Bezout's theorem and its applications in coding theoryGui-Liang Feng · 1996
- 📕Generalized Bezout's theorem and its applications in coding theoryGui-Liang Feng · 1996
- 📕On round-off errors in linear programmingHeiner Müller-Merbach · 1970
Fundamentals of Computer Programming with CSharp Free Book (by Nakov & Co.)Svetlin Nakov · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Singleton bound In coding theory, the Singleton bound, named after the American mathematician Richard Collom Singleton (1928–2007), is a relatively crude upper bound on…
- Decoding methods In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping…
- Coding theory approaches to nucleic acid design DNA code construction refers to the application of coding theory to the design of nucleic acid systems for the field of DNA–based computation. DNA sequences…
- Wozencraft ensemble 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…
- Hamming bound In mathematics and 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…
- Generator matrix 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…
- Locally decodable code A locally decodable code (LDC) is an error-correcting code that allows a single bit of the original message to be decoded with high probability by only…
- Dual 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…