A basis of a polynomial ring (said ring being viewed either as a vector space over the field of coefficients or as a free module over the ring of coefficients).
Definition source: English Wiktionary via Wiktextract
Qualifier: ring theory
Topics: algebra, mathematics, sciences
Examples
- 2007, Nicos Karcanias, Efstathios Milonidis, 2: Structural Methods for Linear Systems: An Introduction, Matthew C. Turner, Declan G. Bates (editors), Mathematical Methods for Robust and Nonlinear Control: EPSRC Summer School, Springer, Lecture Notes in Control and Information Sciences 367, page 89, If T(s)=M(s)D(s)−1 is a RCMFD of T(s), then M(s) is a polynomial basis for X_t. If Q(s) is a greatest right divisor of M(s) then T(s)=◌̅M(s)Q(s)D(s)−1, where ◌̅M(s) is a least degree polynomial basis of X_t [15].
Meaning relationships
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Specifically, a basis, of the form {1, α, ..., αn−1}, of a finite extension F_(qn) of a Galois field F_q, where α is a primitive element of F_(qn) (i.e., a root of a degree-n primitive polynomial over F_q).
Definition source: English Wiktionary via Wiktextract
Qualifier: field theory
Topics: algebra, computing, cryptography, engineering, mathematics, natural-sciences, physical-sciences, sciences
Examples
- 2010, Vladimir Tujillo-Olaya, Jaime Velasco-Medina, Hardware Architectures for Elliptic Curve Cryptoprocessors Using Polynomial and Gaussian Normal Basis Over GF(2233), Marina L. Gravrilova, C. J. Kenneth Tan, Edward David Moreno (editors), Transactions on Computational Science XI: Special Issue on Security in Computing, Part 2, Springer, LNCS 6480, page 79, In this case, the GF(2m) multiplication is implemented in hardware using three algorithms for polynomial basis (PB) and three for gaussian normal basis (GNB).
Meaning relationships
Synonyms: none provided
Antonyms: none provided
