Sentence examples for multiplicative groups of from inspiring English sources

In this paper, we propose signal constellations based on multiplicative groups of Gaussian and Eisenstein integers.

We show that by using multiplicative groups of integers, one can identify and arrange the computation as a pair of convolutions.

Better algorithms based on the index calculus framework have long been known for discrete logarithm problems over multiplicative groups of finite fields or hyperelliptic curves, but generic algorithms have remained the best algorithms for solving ECDLP until recently.

Also, A i ∗ Open image in new window and K i ∗ Open image in new window for each i, where 0 ≤ i ≤ t, are multiplicative groups of units of A i Open image in new window and K i Open image in new window, respectively.

The one parameter group { λ a } is then written with a multiplicative parameter a ∈ R + (the multiplicative group of positive real numbers).

These graphs are constructed using Latin squares defined over a multiplicative group of a Galois ring, rather than a finite field.

The codes are constructed based on regular Tanner graphs by using Latin squares over a multiplicative group of a Galois ring, rather than a finite field.

We consider the infinite-dimensional Lie group G which is the semidirect product of the group of compactly supported diffeomorphisms of a Riemannian manifold X and the commutative multiplicative group of functions on X.

Using the multiplicative group of unit elements of a Galois ring extension of Z p m Open image in new window, Shankar[6] has constructed BCH codes over Z p m Open image in new window.

According to [4, 13, 14], for each integer N ≥ 0, C p N denotes the multiplicative group of the primitive p N th roots of unity in C p ∗ = C p − { 0 }.

We can easily see that f(a b) = f(a f(b) that is f G → R − {0} is a continuous homomorphism of G into the multiplicative group of real numbers.