List of algebraic coding theory topics

This is a list of

algebraic coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data sto ...

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Adler-32 Adler-32 is a checksum algorithm written by Mark Adler in 1995, modifying Fletcher's checksum. Compared to a cyclic redundancy check of the same length, it trades reliability for speed. Adler-32 is more reliable than Fletcher-16, and slightly le ...

* Algebraic geometry code *

BCH code In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called a '' Galois field''). BCH codes were invented in ...

* BCJR algorithm *

Belief propagation Belief propagation, also known as sum–product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for ea ...

* Berger code * Berlekamp–Massey algorithm *

Binary Golay code In mathematics and electronics engineering, a binary 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 a particularly deep and interesting connection ...

* Binary Goppa code *

Bipolar violation A bipolar violation, bipolarity violation, or BPV, is a violation of the bipolar encoding rules where two pulses of the same polarity occur without an intervening pulse of the opposite polarity. This indicates an error in the transmission of t ...

* CRHF * Casting out nines *

Check digit A check digit is a form of redundancy check used for Error detection and correction, error detection on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually. It ...

* Chien's search *

Chipkill __NOTOC__ Chipkill is IBM's trademark for a form of advanced error checking and correcting (ECC) computer memory technology that protects memory systems from single memory chip failures and multi-bit errors from any portion of a single memory chip. ...

* Cksum * Coding gain *

Coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data sto ...

Constant-weight code 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 share the same Hamming weight. The one-hot code and the balanced code are two ...

Convolutional code In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of th ...

* Cross R-S code *

Cryptographic hash function A cryptographic hash function (CHF) is a hash algorithm (a map (mathematics), map of an arbitrary binary string to a binary string with a fixed size of n bits) that has special properties desirable for a cryptography, cryptographic application: ...

Cyclic redundancy check A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital data. Blocks of data entering these systems get a short ''check value'' attached, based on ...

Damm algorithm In error detection, the Damm algorithm is a check digit algorithm that detects all single-digit errors and all adjacent transposition errors. It was presented by H. Michael Damm in 2004, as a part of his PhD dissertation entitled ''Totally Antisy ...

Dual code In coding theory, the dual code of a linear code :C\subset\mathbb_q^n is the linear code defined by :C^\perp = \ where :\langle x, c \rangle = \sum_^n x_i c_i is a scalar product. In linear algebra terms, the dual code is the annihilator ...

* EXIT chart *

Error-correcting code In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The centra ...

* Enumerator polynomial *

Fletcher's checksum The Fletcher checksum is an algorithm for computing a position-dependent checksum devised by John G. Fletcher (1934–2012) at Lawrence Livermore Labs in the late 1970s. The objective of the Fletcher checksum was to provide error-detection prope ...

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Forward error correction In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The centra ...

* Forward-backward algorithm *

Gilbert–Varshamov bound In 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) code. It is occasionally known as the Gilbert– Shannon–Varshamov bound (or the GSV bou ...

* GOST (hash function) * Group coded recording * HAS-160 * HAS-V * HAVAL *

Hadamard code The Hadamard code is an error-correcting code named after the French mathematician Jacques Hadamard that is used for error detection and correction when transmitting messages over very noisy or unreliable channels. In 1971, the code was used ...

* Hagelbarger code *

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 known as the sphere-packing bound or the volume bound from an interpretation in terms of Spher ...

Hamming code In 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 correct one-bit errors without detection of uncorrected errors. By contrast, the ...

Hamming(7,4) In coding theory, Hamming(7,4) is a linear code, linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes, but the term ''Hamming code'' often re ...

Hamming distance In information theory, the Hamming distance between two String (computer science), strings or vectors of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number ...

Hamming weight The Hamming weight of a string (computer science), string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the mo ...

Hash collision In computer science, a hash collision or hash clash is when two distinct pieces of data in a hash table share the same hash value. The hash value in this case is derived from a hash function which takes a data input and returns a fixed length of ...

Hash function A hash function is any Function (mathematics), function that can be used to map data (computing), data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. The values returned by a ...

* Hash list * Hash tree *

Induction puzzles Induction puzzles are logic puzzles, which are examples of Dynamic epistemic logic, multi-agent reasoning, where the solution evolves along with the principle of mathematical induction, induction. A puzzle's scenario always involves multiple pl ...

* Integrity check value * Interleaving *

ISBN The International Standard Book Number (ISBN) is a numeric commercial book identifier that is intended to be unique. Publishers purchase or receive ISBNs from an affiliate of the International ISBN Agency. A different ISBN is assigned to e ...

ISMN The International Standard Music Number or ISMN (ISO 10957) is a thirteen-character alphanumeric identifier for Sheet music, printed music developed by International Organization for Standardization, ISO. Overview The original proposal for an IS ...

LM hash LAN Manager is a discontinued network operating system (NOS) available from multiple vendors and developed by Microsoft in cooperation with 3Com Corporation. It was designed to succeed 3Com's 3+Share network server software which ran atop a h ...

Lexicographic code Lexicographic codes or lexicodes are greedily generated error-correcting codes with remarkably good properties. They were produced independently by Vladimir Levenshtein and by John Horton Conway and Neil Sloane. The binary lexicographic codes are ...

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Linear code In coding theory, a linear code is an error-correcting code for which any linear combination of Code word (communication), codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although t ...

Link adaptation Link adaptation, comprising adaptive coding and modulation (ACM) and others (such as Power Control), is a term used in wireless communications to denote the matching of the modulation, coding and other signal and protocol parameters to the conditi ...

* Low-density parity-check *

Luhn algorithm The Luhn algorithm or Luhn formula (creator: IBM scientist Hans Peter Luhn), also known as the " modulus 10" or "mod 10" algorithm, is a simple check digit formula used to validate a variety of identification numbers. The algorithm is in the pub ...

* Luhn mod N algorithm * M of n codes * MD2 *

MD4 The MD4 Message-Digest Algorithm is a cryptographic hash function developed by Ronald Rivest in 1990. The digest length is 128 bits. The algorithm has influenced later designs, such as the MD5, SHA-1 and RIPEMD algorithms. The initialism "MD" st ...

MD5 The MD5 message-digest algorithm is a widely used hash function producing a 128-bit hash value. MD5 was designed by Ronald Rivest in 1991 to replace an earlier hash function MD4, and was specified in 1992 as Request for Comments, RFC 1321. MD5 ...

* MDC-2 * Majority logic decoding * McWilliams identity *

Md5sum is a computer program that calculates and verifies 128-bit MD5 hashes, as described in RFC 1321. The MD5 hash functions as a compact digital fingerprint of a file. As with all such hashing algorithms, there is theoretically an unlimited number ...

Merkle–Damgård construction In cryptography, the Merkle–Damgård construction or Merkle–Damgård hash function is a method of building collision-resistant cryptographic hash functions from collision-resistant one-way compression functions. This construction was used in t ...

* N-Hash * Negative-acknowledge character *

One-way compression function In cryptography, a one-way compression function is a function that transforms two fixed-length inputs into a fixed-length output.Handbook of Applied Cryptography by Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone. Fifth Printing (August ...

Parity bit A parity bit, or check bit, is a bit added to a string of binary code. Parity bits are a simple form of error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit octets (bytes) ...

* Pearson hashing * Perfect code * Quantum fingerprinting * RIPEMD *

Random oracle In cryptography, a random oracle is an oracle (a theoretical black box) that responds to every ''unique query'' with a (truly) random response chosen uniformly from its output domain. If a query is repeated, it responds the same way every tim ...

* Redundancy check * Reed–Solomon code *

Reed–Solomon error correction 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 in 1960. They have many applications, including consumer technologies such as MiniDiscs, ...

* Repeat-accumulate code , , , valign="top" , *

Repetition 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 may corrupt the transmission in a few places, the idea of the repetition code is to just repeat ...

* SEC-DED * SFV *

SHA-1 In cryptography, SHA-1 (Secure Hash Algorithm 1) is a hash function which takes an input and produces a 160-bit (20-byte) hash value known as a message digest – typically rendered as 40 hexadecimal digits. It was designed by the United States ...

SHA-2 SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published in 2001. They are built using the Merkle–Damgård construction, from a one-way compression ...

Sanity testing A sanity check or sanity test is a basic test to quickly evaluate whether a claim or the result of a calculation can possibly be true. It is a simple check to see if the produced material is rational (that the material's creator was thinking ration ...

* Shaping codes *

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 the size of an arbitrary block code C with block length n, size M and minimum distance d. It ...

* Snake-in-the-box * Snefru * Soft output Viterbi algorithm *

Sparse graph code Sparse is a computer software tool designed to find possible coding faults in the Linux kernel. Unlike List of tools for static code analysis, other such tools, this static code analysis, static analysis tool was initially designed to only flag ...

Syndrome decoding 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 messages to codewords. These are often used to recover messages sent over a noisy channel, ...

Tanner graph {{Short description, 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 codes, error correcting code. Tanner graphs p ...

Ternary Golay code In coding theory, the ternary Golay codes are two closely related error-correcting codes. The code generally known simply as the ternary Golay code is an 1, 6, 53-code, that is, it is a linear code over a ternary alphabet; the relative distan ...

* Tiger (hash function) * Transverse redundancy check *

Triple modular redundancy In computing, triple modular redundancy, sometimes called triple-mode redundancy, (TMR) is a fault-tolerant form of N-modular redundancy, in which three systems perform a process and that result is processed by a majority-voting system to produc ...

* Turbo code * UOWHF *

Universal hashing In mathematics and computing, universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family of hash functions with a certain mathematical property (see definition below). This guarantees ...

Universal Product Code The Universal Product Code (UPC or UPC code) is a barcode#Symbologies, barcode symbology that is used worldwide for tracking trade items in stores. The chosen symbology has bars (or spaces) of exactly 1, 2, 3, or 4 units wide each; each decimal ...

* Verhoeff algorithm * Viterbi algorithm * Viterbi decoder *

WHIRLPOOL A whirlpool is a body of rotating water produced by opposing currents or a current running into an obstacle. Small whirlpools form when a bath or a sink is draining. More powerful ones formed in seas or oceans may be called maelstroms ( ). ''Vo ...

Algebraic coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data sto ...