|
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 Antisymmetric Quasigroups.'' Strengths and weaknesses Strengths The Damm algorithm is similar to the Verhoeff algorithm. It too will detect ''all'' occurrences of the two most frequently appearing types of transcription errors, namely altering a single digit or transposing two adjacent digits (including the transposition of the trailing check digit and the preceding digit). The Damm algorithm has the benefit that it does not have the dedicatedly constructed permutations and its position-specific powers of the Verhoeff scheme. A table of inverses can also be dispensed with when all main diagonal entries of the operation table are zero. The Damm algorithm generates only 10 possible values, avoiding the need for a non-digit character (suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Detection
In information theory and coding theory with applications in computer science and telecommunications, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Definitions ''Error detection'' is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. ''Error correction'' is the detection of errors and reconstruction of the original, error-free data. History In classical antiquity, copyists of the Hebrew Bible were paid for their work according to the number of stichs (lines of verse). As the prose books of the Bible were hardly ever w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order (group Theory)
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is ''infinite''. The ''order'' of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element of a group, is thus the smallest positive integer such that , where denotes the identity element of the group, and denotes the product of copies of . If no such exists, the order of is infinite. The order of a group is denoted by or , and the order of an element is denoted by or , instead of \operatorname(\langle a\rangle), where the brackets denote the generated group. Lagrange's theorem states that for any subgroup of a finite group , the order of the subgroup divides the order of the group; that is, is a divisor of . In particular, the order of any element is a divisor of . Example The symmetric group S3 ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin Squares
Latin ( or ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken by the Latins in Latium (now known as Lazio), the lower Tiber area around Rome, Italy. Through the expansion of the Roman Republic, it became the dominant language in the Italian Peninsula and subsequently throughout the Roman Empire. It has greatly influenced many languages, including English, having contributed many words to the English lexicon, particularly after the Christianization of the Anglo-Saxons and the Norman Conquest. Latin roots appear frequently in the technical vocabulary used by fields such as theology, the sciences, medicine, and law. By the late Roman Republic, Old Latin had evolved into standardized Classical Latin. Vulgar Latin refers to the less prestigious colloquial registers, attested in inscriptions and some literary works such as those of the comic playwrights Plautus and Terence and the author Petronius. While ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Structures
In mathematics, an algebraic structure or algebraic system consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplication), and a finite set of identities (known as ''axioms'') that these operations must satisfy. An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures. For instance, a vector space involves a second structure called a field, and an operation called ''scalar multiplication'' between elements of the field (called '' scalars''), and elements of the vector space (called '' vectors''). Abstract algebra is the name that is commonly given to the study of algebraic structures. The general theory of algebraic structures has been formalized in universal algebra. Category theory is another formalization that includes also other mathematical structures and functions between structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Checksum Algorithms
A checksum is a small-sized block of data derived from another block of digital data for the purpose of detecting errors that may have been introduced during its transmission or storage. By themselves, checksums are often used to verify data integrity but are not relied upon to verify data authenticity. The procedure which generates this checksum is called a checksum function or checksum algorithm. Depending on its design goals, a good checksum algorithm usually outputs a significantly different value, even for small changes made to the input. This is especially true of cryptographic hash functions, which may be used to detect many data corruption errors and verify overall data integrity; if the computed checksum for the current data input matches the stored value of a previously computed checksum, there is a very high probability the data has not been accidentally altered or corrupted. Checksum functions are related to hash functions, fingerprints, randomization functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm Implementation/Checksums/Damm Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an effective method, an algorithm can be expressed within a finite amount of space and time"Any classical mathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Check Digit TA Quasigroup Dhmd111rr Illustration Eg5724
Check or cheque, may refer to: Places * Check, Virginia Arts, entertainment, and media * ''Check'' (film), a 2021 Indian Telugu-language film * "The Check" (''The Amazing World of Gumball''), a 2015 episode of ''The Amazing World of Gumball'' * '' The Checks'' (episode), a 1996 TV episode of ''Seinfeld'' Games and sports * Check (chess), a threat to capture the king or general * Check (poker), declining to bet * Checking (ice hockey), several techniques * Casino chip, less commonly referred to as a check Music * ''The Checks'' (band), a New Zealand band * "Check" (Meek Mill song), 2015 * "Check" (Young Thug song), 2015 * "Check", a song by bbno$, 2025 * "Check", a song by Chris Janson from '' Real Friends'', 2019 * "Check", a song by E-40 from '' The D-Boy Diary: Book 1'', 2016 * "Check", a song by Flo from '' Access All Areas'', 2024 * "Check", a song by Kojo Funds featuring Raye from ''Golden Boy'', 2018 * "Check", a song by Lil Durk from '' Lil Durk 2X'', 2016 * "Check ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasigroup
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that " division" is always possible. Quasigroups differ from groups mainly in that the associative and identity element properties are optional. In fact, a nonempty associative quasigroup is a group. A quasigroup that has an identity element is called a loop. Definitions There are at least two structurally equivalent formal definitions of quasigroup: * One defines a quasigroup as a set with one binary operation. * The other, from universal algebra, defines a quasigroup as having three primitive operations. The homomorphic image of a quasigroup that is defined with a single binary operation, however, need not be a quasigroup, in contrast to a quasigroup as having three primitive operations. We begin with the first definition. Algebra A quasigroup is a non-empty set with a binary operation (that is, a magma, indicating that a quasigroup has to sat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cayley Table
Named after the 19th-century United Kingdom, British mathematician Arthur Cayley, a Cayley table describes the structure of a finite group by arranging all the possible products of all the group's elements in a square table reminiscent of an addition or multiplication table. Many properties of a groupsuch as whether or not it is abelian group, abelian, which elements are inverse element, inverses of which elements, and the size and contents of the group's center (group theory), centercan be discovered from its Cayley table. A simple example of a Cayley table is the one for the group under ordinary multiplication: History Cayley tables were first presented in Cayley's 1854 paper, "On The Theory of Groups, as depending on the symbolic equation ''θ'' ''n'' = 1". In that paper they were referred to simply as tables, and were merely illustrativethey came to be known as Cayley tables later on, in honour of their creator. Structure and layout Because many Cayley tables descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin Square
Latin ( or ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken by the Latins in Latium (now known as Lazio), the lower Tiber area around Rome, Italy. Through the expansion of the Roman Republic, it became the dominant language in the Italian Peninsula and subsequently throughout the Roman Empire. It has greatly influenced many languages, including English, having contributed many words to the English lexicon, particularly after the Christianization of the Anglo-Saxons and the Norman Conquest. Latin roots appear frequently in the technical vocabulary used by fields such as theology, the sciences, medicine, and law. By the late Roman Republic, Old Latin had evolved into standardized Classical Latin. Vulgar Latin refers to the less prestigious colloquial registers, attested in inscriptions and some literary works such as those of the comic playwrights Plautus and Terence and the author Petronius. Whil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasigroup
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that " division" is always possible. Quasigroups differ from groups mainly in that the associative and identity element properties are optional. In fact, a nonempty associative quasigroup is a group. A quasigroup that has an identity element is called a loop. Definitions There are at least two structurally equivalent formal definitions of quasigroup: * One defines a quasigroup as a set with one binary operation. * The other, from universal algebra, defines a quasigroup as having three primitive operations. The homomorphic image of a quasigroup that is defined with a single binary operation, however, need not be a quasigroup, in contrast to a quasigroup as having three primitive operations. We begin with the first definition. Algebra A quasigroup is a non-empty set with a binary operation (that is, a magma, indicating that a quasigroup has to sat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 is analogous to a binary parity bit used to check for errors in computer-generated data. It consists of one or more digits (or letters) computed by an algorithm from the other digits (or letters) in the sequence input. With a check digit, one can detect simple errors in the input of a series of characters (usually digits) such as a single mistyped digit or some permutations of two successive digits. Design Check digit algorithms are generally designed to capture ''human'' transcription errors. In order of complexity, these include the following: * letter/digit errors, such as l → 1 or O → 0 * single-digit errors, such as 1 → 2 * transposition errors, such as 12 → 21 * twin errors, such as 11 → 22 * jump transpositions errors, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
