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Frobenius Fields
The embedding property (Proposition 20.7.4) for free profinite groups is essential to the primitive recursive procedure for perfect PAC fields with...
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The Hilbert–Grunwald specialization property over number fields
Given a finite group G and a number field K , we investigate the following question: Does there exist a Galois extension E/K ( t ) with group G whose set...
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Generalized negacyclic codes over finite fields
Linear codes with additional algebraic structures such as cyclic codes, negacyclic codes and abelian codes have become of interest due to their nice...
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Partially Ordered Fields and Integral Domains
The article studies the division closed partial orders on fields that are algebraic over the field of rational numbers. In particular, the maximal...
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Analysis of periodic linear systems over finite fields with and without Floquet Transform
This paper develops the analysis of discrete-time periodically time-varying linear systems over finite fields. It is shown that the conditions for...
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Multi-twisted additive codes over finite fields
In this paper, we introduce a new class of additive codes over finite fields, viz. multi-twisted (MT) additive codes, which are generalizations of...
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On the approximation of electromagnetic fields by edge finite elements—Part 4: analysis of the model with one sign-changing coefficient
In electromagnetism, in the presence of a negative material surrounded by a classical material, the electric permittivity, and possibly the magnetic...
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Conformal Vector Fields
This chapter is devoted to conformal Killing vector fields, their integrability conditions, their zeros and Lichnerowicz conjecture on...
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Discrete Helmholtz Decompositions of Piecewise Constant and Piecewise Affine Vector and Tensor Fields
Discrete Helmholtz decompositions dissect piecewise polynomial vector fields on simplicial meshes into piecewise gradients and rotations of finite...
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Non-Archimedean Fields
In this chapter, we review some facts from the theory of non-Archimedean fields that will be used in later chapters. We discuss completions, Hensel’s...
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The Lengths of Matrix Incidence Algebras Over Small Finite Fields
The paper considers the problem of computing the lengths of matrix incidence algebras over a field whose cardinality is strictly less than the matrix...
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Degrees and fields of values of irreducible characters
We completely describe all the possible fields of values of irreducible characters of degree up to 3 of finite groups. The obtained result points...
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On pseudorandom subsets in finite fields I: measure of pseudorandomness and support of Boolean functions
Subsets with “good” properties in finite fields are widely applied in coding and cryptography. In this paper we introduce pseudorandom measures for...