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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 distance of the code is as large as it possibly can be for a ternary code, and hence, the ternary Golay code is a perfect code. The extended ternary Golay code is a 2, 6, 6linear code obtained by adding a zero-sum check digit to the 1, 6, 5code. In finite group theory, the extended ternary Golay code is sometimes referred to as the ternary Golay code. Properties Ternary Golay code The ternary Golay code consists of 36 = 729 codewords. Its parity check matrix is : \left[ \begin 1 & 1 & 1 & 2 & 2 & 0 & 1 & 0 & 0 & 0 & 0\\ 1 & 1 & 2 & 1 & 0 & 2 & 0 & 1 & 0 & 0 & 0\\ 1 & 2 & 1 & 0 & 1 & 2 & 0 & 0 & 1 & 0 & 0\\ 1 & 2 & 0 & 1 & 2 & 1 & 0 & 0 & 0 & 1 & 0\\ 1 & 0 & 2 & 2 & 1 & 1 & 0 & 0 & 0 & 0 & 1 \end \right]. Any two differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marcel J
Marcel may refer to: People * Marcel (given name), people with the given name Marcel * Marcel (footballer, born August 1981), Marcel Silva Andrade, Brazilian midfielder * Marcel (footballer, born November 1981), Marcel Augusto Ortolan, Brazilian striker * Marcel (footballer, born 1983), Marcel Silva Cardoso, Brazilian left back * Marcel (footballer, born 1992), Marcel Henrique Garcia Alves Pereira, Brazilian midfielder * Marcel (singer), American country music singer * Étienne Marcel (died 1358), provost of merchants of Paris * Gabriel Marcel (1889–1973), French philosopher, Christian existentialist and playwright * Jean Marcel (died 1980), Madagascan Anglican bishop * Jean-Jacques Marcel (1931–2014), French football player * Rosie Marcel (born 1977), English actor * Sylvain Marcel (born 1974), Canadian actor * Terry Marcel (born 1942), British film director * Claude Marcel (1793-1876), French diplomat and applied linguist Other uses * Marcel (''Friends''), a fiction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automorphism Group
In mathematics, the automorphism group of an object ''X'' is the group consisting of automorphisms of ''X'' under composition of morphisms. For example, if ''X'' is a finite-dimensional vector space, then the automorphism group of ''X'' is the group of invertible linear transformations from ''X'' to itself (the general linear group of ''X''). If instead ''X'' is a group, then its automorphism group \operatorname(X) is the group consisting of all group automorphisms of ''X''. Especially in geometric contexts, an automorphism group is also called a symmetry group. A subgroup of an automorphism group is sometimes called a transformation group. Automorphism groups are studied in a general way in the field of category theory. Examples If ''X'' is a set with no additional structure, then any bijection from ''X'' to itself is an automorphism, and hence the automorphism group of ''X'' in this case is precisely the symmetric group of ''X''. If the set ''X'' has additional struct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 to the theory of finite sporadic groups in mathematics. These codes are named in honor of Marcel J. E. Golay whose 1949 paper introducing them has been called, by E. R. Berlekamp, the "best single published page" in coding theory. There are two closely related binary Golay codes. The extended binary Golay code, ''G''24 (sometimes just called the "Golay code" in finite group theory) encodes 12 bits of data in a 24-bit word in such a way that any 3-bit errors can be corrected or any 7-bit errors can be detected. The other, the perfect binary Golay code, ''G''23, has codewords of length 23 and is obtained from the extended binary Golay code by deleting one coordinate position (conversely, the extended binary Golay code is obtained from t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlekamp–van Lint–Seidel Graph
In graph theory, the Berlekamp–Van Lint–Seidel graph is a locally linear strongly regular graph with parameters (243,22,1,2). This means that it has 243 vertices, 22 edges per vertex (for a total of 2673 edges), exactly one shared neighbor per pair of adjacent vertices, and exactly two shared neighbors per pair of non-adjacent vertices. It was constructed by Elwyn Berlekamp, J. H. van Lint, and as the coset graph of the ternary Golay code. This graph is the Cayley graph of an abelian group. Among abelian Cayley graphs that are strongly regular and have the last two parameters differing by one, it is the only graph that is not a Paley graph. It is also an integral graph, meaning that the eigenvalues of its adjacency matrix are integers. Like the 9\times 9 Sudoku graph it is an integral abelian Cayley graph whose group elements all have order 3, one of a small number of possibilities for the orders in such a graph. There are five possible combinations of parameters for stro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic State Distillation
Magic state distillation is a method for creating more accurate quantum states from multiple noisy ones, which is important for building fault tolerant quantum computers. It has also been linked to quantum contextuality, a concept thought to contribute to quantum computers' power. The technique was first proposed by Emanuel Knill in 2004, and further analyzed by Sergey Bravyi and Alexei Kitaev the same year. Thanks to the Gottesman–Knill theorem, it is known that some quantum operations (operations in the Clifford algebra) can be perfectly simulated in polynomial time on a probabilistic classical computer. In order to achieve universal quantum computation, a quantum computer must be able to perform operations outside this set. Magic state distillation achieves this, in principle, by concentrating the usefulness of imperfect resources, represented by mixed states, into states that are conducive for performing operations that are difficult to simulate classically. A vari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though current quantum computers may be too small to outperform usual (classical) computers for practical applications, larger realizations are believed to be capable of solving certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science. There are several models of quantum computation with the most widely used being quantum circuits. Other models include the quantum Turing machine, quantum annealing, and adiabatic quantum computation. Most models are based on the quantum bit, or " qubit", which is somewhat analogous to the bit in classical computation. A qubit can be in a 1 or 0 quan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magazine
A magazine is a periodical publication, generally published on a regular schedule (often weekly or monthly), containing a variety of content. They are generally financed by advertising, purchase price, prepaid subscriptions, or by a combination of the three. Definition In the technical sense a '' journal'' has continuous pagination throughout a volume. Thus ''Business Week'', which starts each issue anew with page one, is a magazine, but the '' Journal of Business Communication'', which continues the same sequence of pagination throughout the coterminous year, is a journal. Some professional or trade publications are also peer-reviewed, for example the '' Journal of Accountancy''. Non-peer-reviewed academic or professional publications are generally ''professional magazines''. That a publication calls itself a ''journal'' does not make it a journal in the technical sense; ''The Wall Street Journal'' is actually a newspaper. Etymology The word "magazine" derives from Arabic , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Juhani Virtakallio
Juhani is a common Finnish male given name and Arabic surname. Given name * Juhani Aaltonen (born 1935), Finnish jazz saxophonist and flautist * Juhani Aho * Juhani Kaskeala * Juhani Komulainen * Juhani Kumpulainen * Juhani Lahtinen * Juhani "Juice" Leskinen (1950–2006), Finnish musician * Juhani Ojala * Juhani Pallasmaa * Juhani Peltonen * Juhani Suutarinen * Juhani Tamminen * Juhani Tamminen (ice hockey, born 1989) * Juhani Wahlsten Surname * Khalid al-Juhani, Saudi al-Qaeda member * Ma'bad al-Juhani, Islamic figure Fictional characters *Juhani (Star Wars) Juhani is a fictional character appearing in BioWare's 2003 action role-playing video game '' Star Wars: Knights of the Old Republic''. Within the series, Juhani is a Jedi Knight who is a member of the feline Cathar species. She initially appear ..., a female playable character featured in '' Star Wars: Knights of the Old Republic''. * Juhani Otso Berg, a major antagonist in the modern day plotline of the Assa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finland
Finland ( fi, Suomi ; sv, Finland ), officially the Republic of Finland (; ), is a Nordic country in Northern Europe. It shares land borders with Sweden to the northwest, Norway to the north, and Russia to the east, with the Gulf of Bothnia to the west and the Gulf of Finland across Estonia to the south. Finland covers an area of with a population of 5.6 million. Helsinki is the capital and largest city, forming a larger metropolitan area with the neighbouring cities of Espoo, Kauniainen, and Vantaa. The vast majority of the population are ethnic Finns. Finnish, alongside Swedish, are the official languages. Swedish is the native language of 5.2% of the population. Finland's climate varies from humid continental in the south to the boreal in the north. The land cover is primarily a boreal forest biome, with more than 180,000 recorded lakes. Finland was first inhabited around 9000 BC after the Last Glacial Period. The Stone Age introduced several differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steiner System
250px, thumbnail, The Fano plane is a Steiner triple system S(2,3,7). The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and ''t'' = 2 or (recently) ''t'' ≥ 2. A Steiner system with parameters ''t'', ''k'', ''n'', written S(''t'',''k'',''n''), is an ''n''-element set ''S'' together with a set of ''k''-element subsets of ''S'' (called blocks) with the property that each ''t''-element subset of ''S'' is contained in exactly one block. In an alternate notation for block designs, an S(''t'',''k'',''n'') would be a ''t''-(''n'',''k'',1) design. This definition is relatively new. The classical definition of Steiner systems also required that ''k'' = ''t'' + 1. An S(2,3,''n'') was (and still is) called a ''Steiner triple'' (or ''triad'') ''system'', while an S(3,4,''n'') is called a ''Steiner quadr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hadamard Matrix
In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. In geometric terms, this means that each pair of rows in a Hadamard matrix represents two perpendicular vectors, while in combinatorial terms, it means that each pair of rows has matching entries in exactly half of their columns and mismatched entries in the remaining columns. It is a consequence of this definition that the corresponding properties hold for columns as well as rows. The ''n''-dimensional parallelotope spanned by the rows of an ''n''×''n'' Hadamard matrix has the maximum possible ''n''-dimensional volume among parallelotopes spanned by vectors whose entries are bounded in absolute value by 1. Equivalently, a Hadamard matrix has maximal determinant among matrices with entries of absolute value less than or equal to 1 and so is an extremal solution of Hadamard's maximal deter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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