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Topic: Coding theory

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List of mathematical theories

Entropy coding

Huffman coding

Code

Code word

Arithmetic encoding

Information theory

Range encoding

Hamming distance

Data compression

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Quantum information theory

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Recursion theory

List of important publications in computer science

	Coding theory: the first 50 years
		Coding theory is the branch of mathematics concerned with transmitting data across noisy channels and recovering the message.
		His first attempt produced a code in which four data bits were followed by three check bits which allowed not only the detection but the correction of a single error.
		The value of error-correcting codes for information transmission, both on Earth and from space, was immediately apparent, and a wide variety of codes were constructed which achieved both economy of transmission and error-correction capacity.
	pass.maths.org.uk /issue3/codes (1013 words)

	Coding theory - Wikipedia, the free encyclopedia
		Coding theory is a branch of mathematics and computer science dealing with the error-prone process of transmitting data across noisy channels, via clever means, so that a large number of errors that occur can be corrected.
		Cyclic codes (Hamming code, is a subset of cyclic codes)
		The Viterbi algorithm is the optimum algorithm used to decode convolutional codes.
	en.wikipedia.org /wiki/Coding_theory (1757 words)

	Online Encyclopedia and Dictionary - Coding theory (Site not responding. Last check: 2007-10-27)
		Coding theory deals with the properties of codes and thus with their fitness for a specific application.
		The aim of coding theory is to find codes which transmit quickly, contain many valid code words and can correct or at least detect many errors.
		The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then further researched.
	www.fact-archive.com /encyclopedia/Coding_theory (180 words)

	Network coding - Wikipedia, the free encyclopedia
		Network coding is a field of information theory and coding theory and is a method of attaining maximum information flow in a network.
		An example in the paper is not solvable using any linear code over any field size or in any dimension; further, it is not asymptotically linear nor is it linearly solvable using convolutional codes or time-sharing methods.
		This is a linear code because the encoding and decoding schemes are linear operations.
	en.wikipedia.org /wiki/Network_coding (766 words)

	coding theory
		Coding theory is about making messages easy to read and is thus not to be confused with cryptography, which is the art of making messages hard to read!
		In 1948, Claude Shannon, at Bell Labs, started the whole subject of coding theory by proving the minimum number of extra bits that had to be transmitted to encode messages.
		The value of error-correcting codes for information transmission, both on Earth and from space, was immediately apparent, and a wide variety of codes were constructed that achieved both economy of transmission and error-correction capacity.
	www.daviddarling.info /encyclopedia/C/coding_theory.html (636 words)

	HighBeam Encyclopedia - quantum theory
		QUANTUM THEORY [quantum theory] modern physical theory concerned with the emission and absorption of energy by matter and with the motion of material particles; the quantum theory and the theory of relativity together form the theoretical basis of modern physics.
		Just as the theory of relativity assumes importance in the special situation where very large speeds are involved, so the quantum theory is necessary for the special situation where very small quantities are involved, i.e., on the scale of molecules, atoms, and elementary particles.
		According to the older theories of classical physics, energy is treated solely as a continuous phenomenon, while matter is assumed to occupy a very specific region of space and to move in a continuous manner.
	www.encyclopedia.com /html/q/quantumt.asp (873 words)

	Coding theory: the first 50 years
		Coding theory is the branch of mathematics concerned with transmitting data across noisy channels and recovering the message.
		His first attempt produced a code in which four data bits were followed by three check bits which allowed not only the detection but the correction of a single error.
		The value of error-correcting codes for information transmission, both on Earth and from space, was immediately apparent, and a wide variety of codes were constructed which achieved both economy of transmission and error-correction capacity.
	plus.maths.org /issue3/codes (1021 words)

	Data compression - Wikipedia, the free encyclopedia
		In computer science and information theory, data compression or source coding is the process of encoding information using fewer bits (or other information-bearing units) than an unencoded representation would use through use of specific encoding schemes.
		Arithmetic coding, invented by Jorma Rissanen, and turned into a practical method by Witten, Neal, and Cleary, achieves superior compression to the better-known Huffman algorithm, and lends itself especially well to adaptive data compression tasks where the predictions are strongly context-dependent.
		Arithmetic coding is used in the bilevel image-compression standard JBIG, and the document-compression standard DjVu.
	en.wikipedia.org /wiki/Data_compression (1402 words)

	Open Directory - Science: Math: Applications: Communication Theory: Coding Theory
		Coding Theory and Algebraic Geometry: an Interplay - A short explanation of Goppa codes by J. Hirschfeld.
		On Woven Convolutional Codes - Thesis by Stefan Hoest.
		Theory of Codes - Lecture notes from a course taught by Jean Berstel and Dominque Perrin.
	dmoz.org /Science/Math/Applications/Communication_Theory/Coding_Theory (371 words)

	Coding Theory (Site not responding. Last check: 2007-10-27)
		A code C over an alphabet A is a set of vectors of fixed length n with entries from A. A is generally chosen to be a finite field GF(q), and is often in practice just (0,1).
		The rate of a code is the ratio of the number of bits needed to send a message in an error-free transmission to the number needed to send the message using the code.
		One of the goals of coding theory is to find efficient codes, i.e., those that have as large a rate as possible for a given level of error tolerance.
	members.aol.com /jmtsgibbs/ccodethy.htm (451 words)

	Theory of Data Compression
		Lossless data compression theory and rate-distortion theory are known collectively as source coding theory.
		That is, given the code table and given the compressed data, we should be able to rederive the original data.
		The theory assumes that the statistical properties of the source is known.
	www.data-compression.com /theory.shtml (2876 words)

	Application of Statistical Physics to Coding Theory
		Codes on graphs, and specially their prime examples, low-density parity check (LDPC) codes and turbo codes is a research area of great current interest.
		The theory of codes on graphs has not only improved the error performance of communications systems, but it has also opened new research avenues for investigating code constructions and alternative sub-optimal decoding schemes.
		For emerging new coding paradigms to benefit from the achievements made in statistical physics, and for physics to benefit from recent major theoretical advances in coding theory, it is necessary to identify principles and methods unique to both disciplines despite their terminological difference.
	cnls.lanl.gov /~chertkov/FEC.htm (575 words)

	TIP: Theories
		The theory assumes that there are two cognitive subsystems, one specialized for the representation and processing of nonverbal objects/events (i.e., imagery), and the other specialized for dealing with language.
		Dual Coding theory identified three types of processing: (1) representational, the direct activation of verbal or non-verbal representations, (2) referential, the activation of the verbal system by the nonverbal system or vice-versa, and (3) associative processing, the activation of representations within the same verbal or nonverbal system.
		Dual coding theory accounts for the significance of spatial abilities in theories of intelligence (e.g., Guilford).
	tip.psychology.org /paivio.html (380 words)

	Coding Theory and Cryptography
		The coding theory portion deals exclusively with binary codes and codes over fields of characteristic 2, stressing the construction, encoding and decoding of several important families of codes.
		Primarily, we have chosen families of codes that are of interest in engineering and computer science, such as Reed-Solomon codes and convolutional codes, which have been used in deep space communications and consumer electronics (to name but two areas of application).
		In a broad sense, coding theory and cryptography are both concerned with the electronic transfer of information---one with reliability, the other with security.
	www.dms.auburn.edu /faculty/hankerson/ctac/index.html (940 words)

	Coding Theory Group
		Welcome to the home page for the Coding Theory Group at the Department of Mathematics of University of Turku.
		A fundamental problem of coding theory is to determine what message was sent on the basis of the approximation that was received.
		The mathematical coding theory is in part pure basic research, but since the applications are never very far away, many aspects have great significance also on the practical level.
	www.math.utu.fi /research/codingtheory (313 words)

	code.html
		Ternary Codes of Minimum Weight 6, and the Classification of Self-Dual Codes of Length 20, V. Pless, N. Sloane and H. Ward, IEEE Trans.
		On Ternary Self-Dual Codes of Length 24, J. Leon, V. Pless and N. Sloane, IEEE Trans.
		Orbit and Coset Analysis of the Golay and Related Codes, J. Conway and N. Sloane, IEEE Trans.
	www.research.att.com /~njas/doc/code.html (1375 words)

	Coding theory and cryptography at the University of Bergen (Site not responding. Last check: 2007-10-27)
		Coding theory and cryptography at the University of Bergen
		The group for coding theory and cryptography does research on methods to secure data against noise (coding theory) or unautorized reading, changing, falsification etc. (cryptography) during transmission or storage.
		Study coding theory and cryptography at the University of Bergen
	www.ii.uib.no /forskningsgrupper/kode/index-eng.shtml (48 words)

	Coding Theory and Data Integrity - IMS
		The first issue, also called data validity, is covered by coding theory and the second issue, also called data integrity, is covered by cryptology.
		Since coding theory and cryptology can be viewed as related subjects and share a lot of mathematical background, it is meaningful to combine them into a single program.
		Coding and Cryptography — including constructions of codes and nets, asymptotic theory of codes, decoding algorithms, public-key cryptosystems, digital signature schemes, authentication schemes, application of curves and codes to cryptography and issues in cryptanalysis, etc.
	www.ims.nus.edu.sg /Programs/coding (367 words)

	Information Theory and Coding (Site not responding. Last check: 2007-10-27)
		Coding theory, which is the practical realization of the communication limits specified by information theory, will be covered in the second half of the course.
		However, a generalized treatment of coding theory needs knowledge of finite field algebra, which will be hard to cover in a half-semester.
		The second half of the course comprises Hamming codes, cyclic codes (CRC and BCH codes), a brief introduction to Reed-Solomon codes, and perhaps universal codes (Lempel-Ziv coding).
	www.ece.cmu.edu /~negi/courses/18-753.html (262 words)

	C294 Coding Theory and Complexity Theory
		Error-correcting codes and related combinatorial constructs play an important role is several recent (and old) results in complexity theory.
		In most cases, such as in the Goldreich-Levin hard-core predicate construction, the coding theory interpretation became clear only in retrospect, but then it was essential for further improvements.
		This course will be about the theory, constructions, and algorithms for error correcting codes, about applications in complexity theory and in cryptography, and about relations to other combinatorial constructions.
	www.cs.berkeley.edu /~luca/cs294 (567 words)

	Statistics 321: Design Theory and Coding Theory (Site not responding. Last check: 2007-10-27)
		Many designs coeexist with certain families of codes and often the mathematics (group theory, algebra, finite geometry, number theory, and algebraic geometry) used in both the theories have much in common.
		The goal in coding theory has been to provide error-free and secure communication over noisy channels and devise efficient codes and their successful implementation by developing fast encoding and deciding procedures.
		Hamming codes, cyclic codes, BCH codes, Golay codes, Goppa codes, Reed-Muller codes.
	www.stat.unc.edu /321F.html (298 words)

	Why Mathematicians Now Care About Their Hat Color
		Rather, it has deep and unexpected connections to coding theory, an active area of mathematical research with broad applications in telecommunications and computer science.
		In their attempts to devise a complete solution to the problem, researchers are proving new theorems in coding theory that may have applications well beyond mathematical puzzles.
		Dr. Berlekamp, a coding theory expert, said he figured out the solution to the simplest case in about half an hour, but he saw the coding theory connection only while he was falling asleep that night.
	www.msri.org /people/members/sara/articles/hat.html (1519 words)

	Dual Coding Theory: Theoretical Overview and Instructional Application (Site not responding. Last check: 2007-10-27)
		By the late 1960s, psychological theory and research had undergone a pervasive shift away from behaviorism to an emphasis on cognitive processes and their effects in instruction and learning.
		Memory models representing how sensory information is coded began to emerge as a result of various studies related to CIP during the late 60’s.
		Dual Coding Theory proposes that memory consists of two separate but interrelated codes for processing information—one verbal and the other visual.
	chd.gse.gmu.edu /immersion/knowledgebase/strategies/cognitivism/DualCodingTheory.htm (1960 words)

	Introduction to Coding Theory (Site not responding. Last check: 2007-10-27)
		Although its roots lie in information theory, the applications of coding theory now extend to statistics, cryptography, and many areas of pure mathematics, as well as pervading large parts of theoretical computer science, from universal hashing to numerical integration.Introduction to Coding Theory introduces the theory of error-correcting codes in a thorough but gentle presentation.
		The author takes a unique, more natural approach to cyclic codes that is not couched in ring theory but by virtue of its simplicity, leads to far-reaching generalizations.
		Mastering the contents of this book brings a complete understanding of the theory of cyclic codes, including their various applications and the Euclidean algorithm decoding of BCH-codes, and carries readers to the level of the most recent research.
	www.cdqingshan.com /507071.html (414 words)

	The Laws of Cryptography: Coding and Information Theory
		In this case the average code length is the same as the entropy.
		Shannon's theory says that there are other more complicated codes that will also take the error rate arbitrarily close to zero, while maintaining a transmission rate close to 18%.
		Notice the big difference between this code and the triple transmission code: this code has a transmission rate of 50%, while the triple code has a rate of only 33.3%, even though both do single-error correction.
	www.cs.utsa.edu /~wagner/laws/coding.html (2125 words)

	Talk Abstract: Some Connections Between Coding Theory and Cryptography
		This talk will explore some common areas between coding theory and cryptography and attempt to evaluate their status and impact on these disciplines.
		An [n,k] binary code C is a vector space of n-tuples of 0's and 1's of dimension k.
		Vectors in a cyclic code C have these properties if the generator polynomial of the code (characteristic polynomial of the LFSR) is primitive.
	www.ima.umn.edu /cc/wkshp_abstracts/pless/author.html (1210 words)

	Coding (Site not responding. Last check: 2007-10-27)
		A code has a stagger limit of `k' if the synchronisation of all windows of length k+1 or greater is apparent without any more context.
		While the prefix property seems to be quite strict, some fundamental results show that such codes are all that we need to consider for the purposes of inference.
		Arithmetic coding places a limit on the accuracy required; the price is a small loss in coding efficiency and Langdon (1984) states "less than 4%" for the choices in that paper.
	www.csse.monash.edu.au /~lloyd/tildeMML/Notes/Coding.html (1553 words)

	6.896: Essential Coding Theory
		Lecture 03 (09/11): Shannon theory vs. Hamming theory.
		Lecture 11 (10/16): Decoding RS codes, AG codes.
		Lecture 12 (10/21): Decoding AG codes (contd.), Decoding concatenated codes.
	theory.lcs.mit.edu /~madhu/FT02 (298 words)

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