polynomial basis

Noun

 * 1)  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).
 * 2) * 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[right coprime matrix factor description] of $$T(s)$$, then $$M(s)$$ is a polynomial basis for $$\mathfrak X_t$$. If $$Q(s)$$ is a greatest right divisor of $$M(s)$$ then $$T(s) = \overline M(s)Q(s)D(s)^{-1}$$, where $$\overline M(s)$$ is a least degree polynomial basis of $$\mathfrak X_t$$ [15].
 * 1)  Specifically, a basis, of the form { 1, α, ..., αn-1 }, of a finite extension Fqn of a Galois field Fq, where α is a primitive element of Fqn (i.e., a root of a degree-n primitive polynomial over Fq).
 * 2) * 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, 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).
 * 1) * 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, 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).
 * 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).