List of algebraic coding theory topics
Encyclopedia
This is a list of algebraic coding theory topics.
|
> |
Forward error correction In telecommunication, information theory, and coding theory, forward error correction or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels.... Gilbert-Varshamov bound In coding theory, the Gilbert–Varshamov bound is a bound on the parameters of a code . It is occasionally known as the Gilbert–Shannon–Varshamov bound , but the Gilbert–Varshamov bound is by far the most popular name... Gost-Hash The GOST hash function, defined in the standards GOST R 34.11-94 and GOST 34.311-95, is a 256-bit cryptographic hash function. It was initially defined in the Russian national standard GOST R 34.11-94 Information Technology - Cryptographic Information Security - Hash Function... Group Code Recording In computer science, group code recording refers to several distinct but related encoding methods for magnetic media. The first, used in 6250 cpi magnetic tape, is an error-correcting code combined with a run length limited encoding scheme... HAS-160 HAS-160 is a cryptographic hash function designed for use with the Korean KCDSA digital signature algorithm. It is derived from SHA-1, with assorted changes intended to increase its security. It produces a 160-bit output.... HAS-V HAS-V is a cryptographic hash function with a variable output length. HAS-V is a hash function based on a block cipher. The hash function can produce hash values with lengths from 16 to 40 bytes.- Specifications :Digest Size: 128-320 bitsMax message length:... HAVAL HAVAL is a cryptographic hash function. Unlike MD5, but like most modern cryptographic hash functions, HAVAL can produce hashes of different lengths. HAVAL can produce hashes in lengths of 128 bits, 160 bits, 192 bits, 224 bits, and 256 bits... Hadamard code The Hadamard code is an error-correcting code that is used for error detection and correction when transmitting messages over very noisy or unreliable channels.... Hagelbarger code In telecommunication, a Hagelbarger code is a convolutional code that enables error bursts to be corrected provided that there are relatively long error-free intervals between the error bursts.... 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 packing balls in the Hamming metric into the space of... Hamming code In telecommunication, Hamming codes are a family of linear error-correcting codes that generalize the Hamming-code invented by Richard Hamming in 1950. Hamming codes can detect up to two and correct up to one bit errors. By contrast, the simple parity code cannot correct errors, and can detect only... Hamming(7,4) In coding theory, Hamming is a linear error-correcting code that encodes 4 bits of data into 7 bits by adding 3 parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950... Hamming distance In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different... Hamming weight The Hamming weight of a 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 most typical case, a string of bits, this is the number of 1's in the string... Hash collision Not to be confused with wireless packet collision.In computer science, a collision or clash is a situation that occurs when two distinct pieces of data have the same hash value, checksum, fingerprint, or cryptographic digest.... Hash function A hash function is any algorithm or subroutine that maps large data sets to smaller data sets, called keys. For example, a single integer can serve as an index to an array... Hash list In computer science, a hash list is typically a list of hashes of the data blocks in a file or set of files. Lists of hashes are used for many different purposes, such as fast table lookup and distributed databases... Hash tree In cryptography and computer science Hash trees or Merkle trees are a type of data structure which contains a tree of summary information about a larger piece of data – for instance a file – used to verify its contents. Hash trees are a combination of hash lists and hash chaining, which in turn are... Interleaving In computer science and telecommunication, interleaving is a way to arrange data in a non-contiguous way to increase performance.It is typically used:* In error-correction coding, particularly within data transmission, disk storage, and computer memory.... International Standard Book Number The International Standard Book Number is a unique numeric commercial book identifier based upon the 9-digit Standard Book Numbering code created by Gordon Foster, Emeritus Professor of Statistics at Trinity College, Dublin, for the booksellers and stationers W.H... International Standard Music Number The International Standard Music Number or ISMN is a thirteen-character alphanumeric identifier for printed music developed by ISO... LM hash LM hash, LanMan, or LAN Manager hash was the primary hash that Microsoft LAN Manager and Microsoft Windows versions prior to Windows NT used to store user passwords... Lexicographic code Lexicographic codes or lexicodes are greedily generated error-correcting codes with remarkably good properties. They were produced independently byLevenshtein and Conway and Sloane and are known to be linear over some finite fields.- Construction :... |
> |
Linear 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... Link adaptation Link adaptation, or adaptive coding and modulation , is a term used in wireless communications to denote the matching of the modulation, coding and other signal and protocol parameters to the conditions on the radio link Link adaptation, or adaptive coding and modulation (ACM), is a term used in... Low-density parity-check code In information theory, a low-density parity-check code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel, and is constructed using a sparse bipartite graph... Luhn algorithm The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm,is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, National Provider Identifier numbers in US and Canadian Social Insurance Numbers... Luhn mod N algorithm The Luhn mod N algorithm is an extension to the Luhn algorithm that allows it to work with sequences of non-numeric characters... 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.... MD5 The MD5 Message-Digest Algorithm is a widely used cryptographic hash function that produces a 128-bit hash value. Specified in RFC 1321, MD5 has been employed in a wide variety of security applications, and is also commonly used to check data integrity... MDC-2 In cryptography, MDC-2 is a cryptographic hash function. MDC-2 is a hash function based on a block cipher with a proof of security in the ideal-cipher model... Majority logic decoding In error detection and correction, majority logic decoding is a method to decode repetition codes, based on the assumption that the largest number of occurrences of a symbol was the transmitted symbol.-Theory:... Md5sum 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 of files that will have any given MD5 hash... N-Hash In cryptography, N-Hash is a cryptographic hash function based on the FEAL round function, and is now considered insecure. It was proposed in 1990 by Miyaguchi et al.; weaknesses were published the following year.... Negative-acknowledge character * In telecommunications, a negative-acknowledge character is a transmission control character sent by a station as a negative response to the station with which the connection has been set up.... Parity bit A parity bit is a bit that is added to ensure that the number of bits with the value one in a set of bits is even or odd. Parity bits are used as the simplest form of error detecting code.... Pearson hashing Pearson hashing is a hash function designed for fast execution on processors with 8-bit registers. Given an input consisting of any number of bytes, it produces as output a single byte that is strongly dependent on every byte of the input... Quantum fingerprinting Quantum fingerprinting is a proposed technique that uses a quantum computer to generate a string with a similar function to the cryptographic hash function.... RIPEMD RIPEMD-160 is a 160-bit message digest algorithm developed in Leuven, Belgium, by Hans Dobbertin, Antoon Bosselaers and Bart Preneel at the COSIC research group at the Katholieke Universiteit Leuven, and first published in 1996... Random oracle In cryptography, a random oracle is an oracle that responds to every query with a random response chosen uniformly from its output domain, except that for any specific query, it responds the same way every time it receives that query... Reed–Solomon error correction In coding theory, Reed–Solomon codes are non-binary cyclic error-correcting codes invented by Irving S. Reed and Gustave Solomon. They described a systematic way of building codes that could detect and correct multiple random symbol errors... Repeat-Accumulate Code In computer science, repeat-accumulate codes are a low complexity class of error-correcting codes. They were devised so that their ensemble weight distributions are easy to derive... |
> |
Repetition code In coding theory, the repetition code is one of the most basic 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 the message several times. The hope is that the channel... SHA-2 In cryptography, SHA-2 is a set of cryptographic hash functions designed by the National Security Agency and published in 2001 by the NIST as a U.S. Federal Information Processing Standard. SHA stands for Secure Hash Algorithm. SHA-2 includes a significant number of changes from its predecessor,... Shaping codes In digital communications shaping codes are a method of encoding that changes the distribution of signals to improve efficiency.-Description:... Singleton bound In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude bound on the size of a block code C with block length n, size r and minimum distance d.-Statement of the Bound:... Snake-in-the-box The snake-in-the-box problem in graph theory and computer science deals with finding a certain kind of path along the edges of a hypercube. This path starts at one corner and travels along the edges to as many corners as it can reach. After it gets to a new corner, the previous corner and all of... Snefru Snefru is a cryptographic hash function invented by Ralph Merklein 1990which supports 128-bit and 256-bit output. It was named after the Egyptian Pharaoh Sneferu, continuing the tradition of the Khufu and Khafre block ciphers.... Soft output Viterbi algorithm The soft output Viterbi algorithm is a variant of the classical Viterbi algorithm.SOVA differs from the classical Viterbi algorithm in that it uses a modified path metric which takes into account the a priori probabilities of the input symbols, and produces a soft output indicating the reliability... Sparse graph 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 - a set representing the transmitted bits and another set representing the constraints that the transmitted bits have to satisfy... Tanner graph A Tanner graph is a bipartite graph used to state constraints or equations which specify error correcting codes. In coding theory, Tanner graphs are used to construct longer codes from smaller ones... Ternary Golay code There are two closely related error-correcting codes known as ternary Golay codes. The code generally known simply as the ternary Golay code is a perfect [11, 6, 5] ternary linear code; the extended ternary Golay code is a [12, 6, 6] linear code obtained by adding a zero-sum check digit to the... Tiger (hash) In cryptography, Tiger is a cryptographic hash function designed by Ross Anderson and Eli Biham in 1995 for efficiency on 64-bit platforms. The size of a Tiger hash value is 192 bits. Truncated versions can be used for compatibility with protocols assuming a particular hash size... Transverse redundancy check In telecommunications, a transverse redundancy check or vertical redundancy check is a redundancy check for synchronized parallel bits applied once per bit time, across the bit streams... Triple modular redundancy In computing, triple modular redundancy is a fault tolerant form of N-modular redundancy, in which three systems perform a process and that result is processed by a voting system to produce a single output. If any one of the three systems fails, the other two systems can correct and mask the... Turbo code In information theory, turbo codes are a class of high-performance forward error correction codes developed in 1993, which were the first practical codes to closely approach the channel capacity, a theoretical maximum for the code rate at which reliable communication is still possible given a... UOWHF In cryptography a universal one-way hash function , is a type of universal hash function of particular importance to cryptography. UOWHF's are proposed as an alternative to collision-resistant hash functions... Universal hashing Using universal hashing refers to selecting a hash function at random from a family of hash functions with a certain mathematical property . This guarantees a low number of collisions in expectation, even if the data is chosen by an adversary... Universal Product Code The Universal Product Code is a barcode symbology , that is widely used in North America, and in countries including the UK, Australia, and New Zealand for tracking trade items in stores. Its most common form, the UPC-A, consists of 12 numerical digits, which are uniquely assigned to each trade item... Verhoeff algorithm The Verhoeff algorithm, a checksum formula for error detection first published in 1969, was developed by Dutch mathematician Jacobus Verhoeff . Like the more widely known Luhn algorithm, it works with strings of decimal digits of any length... Viterbi algorithm The Viterbi algorithm is a dynamic programming algorithm for finding the most likely sequence of hidden states – called the Viterbi path – that results in a sequence of observed events, especially in the context of Markov information sources, and more generally, hidden Markov models... Viterbi decoder A Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has beenencoded using forward error correction based on a convolutional code.... WHIRLPOOL In computer science and cryptography, Whirlpool is a cryptographic hash function designed by Vincent Rijmen and Paulo S. L. M. Barreto first described in 2000. The hash has been recommended by the NESSIE project... |