Algebraic geometry code information

Algebraic geometry codes, often abbreviated AG codes, are a type of linear code that generalize Reed–Solomon codes. The Russian mathematician V. D. Goppa...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

of general type Zariski surface Algebraic variety Hypersurface Quadric (algebraic geometry) Dimension of an algebraic variety Hilbert's Nullstellensatz...

methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc.—or...

Networks. AN codes Algebraic geometry code BCH code, which can be designed to correct any arbitrary number of errors per code block. Barker code used for...

This is a list of algebraic coding theory topics....

sets, or finite geometries. On the algebraic side, besides group theory and representation theory, lattice theory and commutative algebra are commonly used...

Bose–Chaudhuri–Hochquenghem, Turbo, Golay, algebraic geometry codes, low-density parity-check codes, and space–time codes. Error detecting codes can be optimised to detect...

where the properties of codes are expressed in algebraic terms and then further researched.[citation needed] Algebraic coding theory is basically divided...

for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics...

Galois cohomology of algebraic groups, the spinor norm is a connecting homomorphism on cohomology. Writing μ2 for the algebraic group of square roots...

operator algebras are often phrased in algebraic terms, while the techniques used are often highly analytic. Although the study of operator algebras is usually...

geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry...

early geometry. (See Areas of mathematics and Algebraic geometry.) The earliest recorded beginnings of geometry can be traced to early peoples, such as the...

theory and linear algebra taught in a first degree course, as well as a little projective geometry, and a very little algebraic geometry." When q is a prime...

mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings...

programming; relational algebra used in databases; discrete and finite versions of groups, rings and fields are important in algebraic coding theory; discrete...

binary Goppa codes (subfield codes of algebraic geometry codes of a genus-0 curve over finite fields of characteristic 2); these codes can be efficiently...

polynomials 13: Commutative algebra (Commutative rings and algebras) 14: Algebraic geometry 15: Linear and multilinear algebra; matrix theory 16: Associative...

algebra. Algebraic combinatorics has come to be seen more expansively as an area of mathematics where the interaction of combinatorial and algebraic methods...

representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory[citation needed], combinatorics and number theory. Within...

mathematics, derived noncommutative algebraic geometry, the derived version of noncommutative algebraic geometry, is the geometric study of derived categories...

In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also...

versions Polynomial codes, of which BCH codes are an example Reed–Solomon codes Reed–Muller codes Algebraic geometry codes Binary Goppa codes Low-density parity-check...

differential geometry and topology Glossary of general topology Glossary of Riemannian and metric geometry Glossary of scheme theory List of algebraic geometry topics...

relation between algebraic geometry and codes, utilizing the Riemann-Roch theorem. Today these codes are called algebraic geometry codes. In 1981 he presented...

Acyclic models theorem (algebraic topology) Addition theorem (algebraic geometry) Adiabatic theorem (physics) Ado's theorem (Lie algebra) Akhiezer's theorem...