Binary Golay codeIn 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.
Sequence spaceIn functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication.
AutoCADAutoCAD is a 2D and 3D computer-aided design (CAD) software application for desktop, web, and mobile developed by Autodesk. It was first released in December 1982 for the CP/M and IBM PC platforms as a desktop app running on microcomputers with internal graphics controllers. Initially a DOS application, subsequent versions were later released for other platforms including Classic Mac OS (1992), Microsoft Windows (1992), web browsers (2010), iOS (2010), macOS (2010), and Android (2011).
Banach spaceIn mathematics, more specifically in functional analysis, a Banach space (pronounced ˈbanax) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly.
MindThe mind (adjective form: mental) is that which thinks, imagines, remembers, wills, and senses, or is the set of faculties responsible for such phenomena. The mind is also associated with experiencing perception, pleasure and pain, belief, desire, intention, and emotion. The mind can include conscious and non-conscious states as well as sensory and non-sensory experiences. The exact nature of the mind is disputed. Traditionally, minds were understood as substances, but contemporary philosophers tend to see them as collections of properties or capacities.
Coding theoryCoding 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.
Fréchet spaceIn functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that are complete with respect to the metric induced by the norm). All Banach and Hilbert spaces are Fréchet spaces. Spaces of infinitely differentiable functions are typical examples of Fréchet spaces, many of which are typically Banach spaces.
IntelliCADIntelliCAD is a CAD editor and development platform with an Application Programming Interface API published by the IntelliCAD Technology Consortium ("ITC") through shared development. IntelliCAD emulates the basic interface and functions of AutoCAD, however, it is particularly able to incorporate and interchange freely between a wide variety of file types (i.e. dwg., BIM, TIFF, etc.).
Quantum error correctionQuantum error correction (QEC) is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve fault tolerant quantum computing that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum preparation, and faulty measurements. This would allow algorithms of greater circuit depth. Classical error correction employs redundancy.
Quantum dotQuantum dots (QDs) – also called semiconductor nanocrystals, are semiconductor particles a few nanometres in size, having optical and electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanotechnology and materials science. When the quantum dots are illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conductance band.
Stabilizer codeThe theory of quantum error correction plays a prominent role in the practical realization and engineering of quantum computing and quantum communication devices. The first quantum error-correcting codes are strikingly similar to classical block codes in their operation and performance. Quantum error-correcting codes restore a noisy, decohered quantum state to a pure quantum state. A stabilizer quantum error-correcting code appends ancilla qubits to qubits that we want to protect.
