Sentence examples for field of order from inspiring English sources

One crucial step is the selection of a nonconventional basis for the representation of the field of order 2m over the field of order 2, a fact which almost contradicts the elementary theorem that the Galois field of order 2m is unique, and that all bases define the same field.

It is shown that the row spaces of certain generalized weighing matrices, Bhaskar Rao designs, and generalized Hadamard matrices over a finite field of order q are hermitian self-orthogonal codes.

To address this problem, this work presents methodological and practical proposals for jointly simulating a grade and a rock type, when the former is represented by the transform of a stationary Gaussian random field and the latter is obtained by truncating an intrinsic random field of order k with Gaussian generalized increments.

A subspace bitrade of type Tq t,k,v) is a pair (T0,T1) of two disjoint nonempty collections of k-dimensional subspaces of a v-dimensional space V over the finite field of order q such that every t-dimensional subspace of V is covered by the same number of subspaces from T0 and T1.

For every prime power q, where q≡1(mod4), and p a prime dividing q+12, we construct a self-orthogonal [2q,q−1] code and a self-dual [2q+2,q+1] code over the field of order p. The construction involves Paley graphs and the constructed [2q,q−1] and [2q+2,q+1] codes admit an automorphism group Σ q) of the Paley graph of order q.

We denote by the finite field (Galois field) of order.

This paper presents the design of a new multiplier architecture for normal integer multiplication of positive and negative numbers as well as for multiplication in finite fields of order 2n.

We seek here to compare measurements at low and high field and consider how changes from the transfer field, BS, (of order 10 3 T) to the measurements fields affects the results.

Zeeman splitting has been detected in five hydroxyl megamasers, and the typical strength of a detected field is of order a few milligauss, similar to the field strengths measured in galactic hydroxyl masers.

Obviously, combination of enhanced near-fields of ordered plasmonic nanostructures with unusual optoelectronic properties of graphene will provide a more promising application for novel graphene-based optoelectronic devices, and thus, research on the plasmonic coupling between graphene and plasmonic ordered nanoparticles is highly desirable.

To address the issues associated with computational efficiency, the field of Reduced Order Modelling (ROM) is evolving quickly.