Galois rings and algebraic cryptography
Gauss sum for the adjoint representation of and
Gauss sums and solutions to simultaneous equations over
Gauss sums and the matrix equation over fields of characteristic two
Gauss sums for Fq[T].
Gauss sums for O⁺(2n,q)
Gauss sums for O⁻(2n,q)
Gauss sums for orthogonal groups over a finite field of characteristic two
Gauss sums for prime powers in p-adic fields
Gauss Sums for Symplectic Groups Over a Finite Field.
Gauss Sums of Cubic Characters over , p Odd
An elementary approach is shown which derives the values of the Gauss sums over , p odd, of a cubic character. New links between Gauss sums over different field extensions are shown in terms of factorizations of the Gauss sums themselves, which are then revisited in terms of prime ideal decompositions. Interestingly, one of these results gives a representation of primes p of the form 6k+1 by a binary quadratic form in integers of a subfield of the cyclotomic field of the pth roots of unity.
Gauss Sums of the Cubic Character over : an Elementary Derivation
By an elementary approach, we derive the value of the Gauss sum of a cubic character over a finite field without using Davenport-Hasse’s theorem (namely, if s is odd the Gauss sum is -1, and if s is even its value is ).
Gaussian sums over finite fields and gamma functions. (Gaussche Summen über endlichen Körpern und Gammafunktion.)
Généralisation d'un théorème de I. M. Vinogradov à un corps de séries formelles sur un corps fini
Generalizations of the classical Chebyshev polynomials to polynomials in two variables
Generalized Jacobsthal sums and sums of squares
Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication
A fractional differential controller for incommensurate fractional unified chaotic system is described and proved by using the Gershgorin circle theorem in this paper. Also, based on the idea of a nonlinear observer, a new method for generalized synchronization (GS) of this system is proposed. Furthermore, the GS technique is applied in secure communication (SC), and a chaotic masking system is designed. Finally, the proposed fractional differential controller, GS and chaotic masking scheme are...
Generating linear spans over finite fields
GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation
The Legendre symbol has been used to construct sequences with ideal cross-correlation, but it was never used in the arithmetic cross-correlation. In this paper, a new class of generalized Legendre sequences are described and analyzed with respect to their period, distributional, arithmetic cross-correlation and distinctness properties. This analysis gives a new approach to study the connection between the Legendre symbol and the arithmetic cross-correlation. In the end of this paper, possible application...
Graphes de Ramanujan et applications