Related papers: Generators of finite fields with prescribed traces
A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…
The genesis of spurious solutions in finite basis approximations to operators which possess a continuum and a point spectrum is discussed and a simple solution for identifying these solutions is suggested.
The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field $(K,\nu)$ and an extension $\omega$ of $\nu$ to a finite extension $L$ of $K$.…
Given a multiparameter filtration of simplicial complexes, we consider the problem of explicitly constructing generators for the multipersistent homology groups with arbitrary PID coefficients. We propose the use of spanning trees as a tool…
We study in this paper the sufficient conditions for enhanced continuity of random fields, i.e. such that the modulus of its continuity allows the factorable representation by the product of random variable on the deterministic module of…
We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with $q$ elements and give additive codes over the field with $q^h$ elements whose minimum distance is…
In this paper we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. We give bounds on the order, base size, minimal degree, fixity, and chief length of an arbitrary…
We present a sharp upper bound for the number of generators of a finite group in terms of the ratio between the order and the exponent.
Finite fields form an important chapter in abstract algebra, and mathematics in general. We aim to provide a geometric and intuitive model for finite fields, involving algebraic numbers, in order to make them accessible and interesting to a…
In this paper we extend the relation between convolutional codes and linear systems over finite fields to certain commutative rings through first order representations . We introduce the definition of rings with representations as those for…
We study the existence of primes and of primitive divisors in classical divisibility sequences defined over function fields. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields…
We consider the linear vector space formed by the elements of the finite fields $\mathbb{F}_q$ with $q=p^r$ over $\mathbb{F}_p$. Let ${a_1,\ldots,a_r}$ be a basis of this space. Then the elements $x$ of $\mathbb{F}_q$ have a unique…
Magnetic fields appear everywhere in the universe. From stars and galaxies, all the way to galaxy clusters and remote protogalactic clouds magnetic fields of considerable strength and size have been repeatedly observed. Despite their…
For $q$ an odd prime power, we prove that there are always four consecutive primitive elements in the finite field $\mathbb{F}_{q}$ when $q> 2401$.
We construct and study fields F with the property that F has infinitely many extensions of some fixed degree, but E*/(E*)^n is finite for every finite extension E of F and every n>0.
We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…
This paper makes a comprehensive survey of results relating to finite Rees index for semigroups. In particular, we survey of the state of knowledge on whether various finiteness properties (such as finite generation, finite presentability,…
We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…
In this expository article we collect the integer sequences that count several different types of matrices over finite fields and provide references to the Online Encyclopedia of Integer Sequences (OEIS). Section 1 contains the sequences,…
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…