finite field with q elements

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• Finite field — In abstract algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains only finitely many elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and… …   Wikipedia

• Finite field arithmetic — Arithmetic in a finite field is different from standard integer arithmetic. There are a limited number of elements in the finite field; all operations performed in the finite field result in an element within that field.While each finite field is …   Wikipedia

• Field with one element — In mathematics, the field with one element is a suggestive name for an object that should exist: many objects in math have properties analogous to objects over a field with q elements, where q = 1, and the analogy between number fields and… …   Wikipedia

• Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

• Finite group — In mathematics, a finite group is a group which has finitely many elements. Some aspects of the theory of finite groups were investigated in great depth in the twentieth century, in particular the local theory, and the theory of solvable groups… …   Wikipedia

• Field of definition — In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong. Given polynomials, with coefficients in a field K , it may not be obvious… …   Wikipedia

• Quadratic field — In algebraic number theory, a quadratic field is an algebraic number field K of degree two over Q. It is easy to show that the map d ↦ Q(√d) is a bijection from the set of all square free integers d ≠ 0, 1 to the set of… …   Wikipedia

• Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… …   Wikipedia

• Field of sets — Set algebra redirects here. For the basic properties and laws of sets, see Algebra of sets. In mathematics a field of sets is a pair where X is a set and is an algebra over X i.e., a non empty subset of the power set of X closed under the… …   Wikipedia

• Finite state machine — A finite state machine (FSM) or finite state automaton (plural: automata ) or simply a state machine, is a model of behavior composed of a finite number of states, transitions between those states, and actions. A finite state machine is an… …   Wikipedia

• Finite-state machine — State machine redirects here. For infinite state machines, see State transition system. For fault tolerance methodology, see State machine replication. SFSM redirects here. For the Italian railway company, see Circumvesuviana. A finite state… …   Wikipedia