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Covering Code
In coding theory, a covering code is a set of elements (called ''codewords'') in a space, with the property that every element of the space is within a fixed distance of some codeword. Definition Let q\geq 2, n\geq 1, R\geq 0 be integers. A code C\subseteq Q^n over an alphabet ''Q'' of size , ''Q'', = ''q'' is called ''q''-ary ''R''-covering code of length ''n'' if for every word y\in Q^n there is a codeword x\in C such that the Hamming distance d_H(x,y)\leq R. In other words, the spheres (or balls or rook-domains) of radius ''R'' with respect to the Hamming metric around the codewords of ''C'' have to exhaust the finite metric space Q^n. The covering radius of a code ''C'' is the smallest ''R'' such that ''C'' is ''R''-covering. Every perfect code is a covering code of minimal size. Example ''C'' = is a 5-ary 2-covering code of length 4. Covering problem The determination of the minimal size K_q(n,R) of a ''q''-ary ''R''-covering code of length ''n'' is a very hard ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. There are four types of coding: # Data compression (or ''source coding'') # Error control (or ''channel coding'') # Cryptographic coding # Line coding Data compression attempts to remove unwanted redundancy from the data from a source in order to transmit it more efficiently. For example, ZIP data compression makes data files smaller, for purposes such as to reduce Internet traffic. Data compression a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Combinatorial Theory
The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applications of combinatorics. ''Series B'' is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and are widely known as ''JCTA'' and ''JCTB''. The journal was founded in 1966 by Frank Harary and Gian-Carlo Rota.They are acknowledged on the journals' title pages and Web sites. SeEditorial board of JCTA Originally there was only one journal, which was split into two parts in 1971 as the field grew rapidly. An electronic, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subset
In mathematics, Set (mathematics), set ''A'' is a subset of a set ''B'' if all Element (mathematics), elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they are unequal, then ''A'' is a proper subset of ''B''. The relationship of one set being a subset of another is called inclusion (or sometimes containment). ''A'' is a subset of ''B'' may also be expressed as ''B'' includes (or contains) ''A'' or ''A'' is included (or contained) in ''B''. A ''k''-subset is a subset with ''k'' elements. The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra (structure), Boolean algebra under the subset relation, in which the join and meet are given by Intersection (set theory), intersection and Union (set theory), union, and the subset relation itself is the Inclusion (Boolean algebra), Boolean inclusion relation. Definition If ''A'' and ''B'' are sets and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Telecommunications
Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that feasible with the human voice, but with a similar scale of expediency; thus, slow systems (such as postal mail) are excluded from the field. The transmission media in telecommunication have evolved through numerous stages of technology, from beacons and other visual signals (such as smoke signals, semaphore telegraphs, signal flags, and optical heliographs), to electrical cable and electromagnetic radiation, including light. Such transmission paths are often divided into communication channels, which afford the advantages of multiplexing multiple concurrent communication sessions. ''Telecommunication'' is often used in its plural form. Other examples of pre-modern long-distance communication included audio messages, such as coded drumb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speech Coding
Speech coding is an application of data compression of digital audio signals containing speech. Speech coding uses speech-specific parameter estimation using audio signal processing techniques to model the speech signal, combined with generic data compression algorithms to represent the resulting modeled parameters in a compact bitstream. Some applications of speech coding are mobile telephony and voice over IP (VoIP). The most widely used speech coding technique in mobile telephony is linear predictive coding (LPC), while the most widely used in VoIP applications are the LPC and modified discrete cosine transform (MDCT) techniques. The techniques employed in speech coding are similar to those used in audio data compression and audio coding where knowledge in psychoacoustics is used to transmit only data that is relevant to the human auditory system. For example, in voiceband speech coding, only information in the frequency band 400 to 3500 Hz is transmitted but the reconst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Football Pools
In the United Kingdom, the football pools, often referred to as "the pools", is a betting pool based on predicting the outcome of association football matches taking place in the coming week. The pools are typically cheap to enter, and may encourage gamblers to enter several bets. The traditional and most popular game was the Treble Chance, now branded the Classic Pools game. Players pick 10, 11 or 12 football games from the offered fixtures to finish as a draw, in which each team scores at least one goal. The player with the most accurate predictions wins the top prize, or a share of it if more than one player has these predictions. In addition, there is a special £3,000,000 prize or share of it for correctly predicting the nine score draws (draws of 1-1 or higher) when these are the only score draws on the coupon. Players can win large cash prizes in a variety of other ways, under a points-based scoring system. Entries were traditionally submitted through the post or via agen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Broadcasting
Broadcasting is the distribution (business), distribution of sound, audio or video content to a dispersed audience via any electronic medium (communication), mass communications medium, but typically one using the electromagnetic spectrum (radio waves), in a :wikt:one-to-many, one-to-many model. Broadcasting began with AM radio, which came into popular use around 1920 with the spread of vacuum tube radio transmitters and radio receiver, receivers. Before this, all forms of electronic communication (early radio, telephone, and telegraph) were wikt:one-to-one, one-to-one, with the message intended for a single recipient. The term ''broadcasting'' evolved from its use as the agricultural method of sowing seeds in a field by casting them broadly about. It was later adopted for describing the widespread distribution of information by printed materials or by telegraph. Examples applying it to "one-to-many" radio transmissions of an individual station to multiple listeners appeared as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Code
In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication channel or storage in a storage medium. An early example is an invention of language, which enabled a person, through speech, to communicate what they thought, saw, heard, or felt to others. But speech limits the range of communication to the distance a voice can carry and limits the audience to those present when the speech is uttered. The invention of writing, which converted spoken language into visual symbols, extended the range of communication across space and time. The process of encoding converts information from a source into symbols for communication or storage. Decoding is the reverse process, converting code symbols back into a form that the recipient understands, such as English or/and Spanish. One reason for coding is to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Compression
In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information. Typically, a device that performs data compression is referred to as an encoder, and one that performs the reversal of the process (decompression) as a decoder. The process of reducing the size of a data file is often referred to as data compression. In the context of data transmission, it is called source coding; encoding done at the source of the data before it is stored or transmitted. Source coding should not be confused with channel coding, for error detection and correction or line coding, the means for mapping data onto a signal. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distortion
In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal representing sound or a video signal representing images, in an electronic device or communication channel. Distortion is usually unwanted, and so engineers strive to eliminate or minimize it. In some situations, however, distortion may be desirable. For example, in noise reduction systems like the Dolby system, an audio signal is deliberately distorted in ways that emphasize aspects of the signal that are subject to electrical noise, then it is symmetrically "undistorted" after passing through a noisy communication channel, reducing the noise in the received signal. Distortion is also used as a musical effect, particularly with electric guitars. The addition of noise or other outside signals (hum, interference) is not considered di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elsevier
Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell'', the ScienceDirect collection of electronic journals, '' Trends'', the '' Current Opinion'' series, the online citation database Scopus, the SciVal tool for measuring research performance, the ClinicalKey search engine for clinicians, and the ClinicalPath evidence-based cancer care service. Elsevier's products and services also include digital tools for data management, instruction, research analytics and assessment. Elsevier is part of the RELX Group (known until 2015 as Reed Elsevier), a publicly traded company. According to RELX reports, in 2021 Elsevier published more than 600,000 articles annually in over 2,700 journals; as of 2018 its archives contained over 17 million documents and 40,000 e-books, with over one billion annual downloads. Researchers have criticized Elsevier for its high profit marg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
