• Journal of the Korean Institute of Telematics and Electronics
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• v.17 no.3
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• pp.45-51
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• 1980

In this paper, a method for constructing Galois switching functions is presented. Single variable Galois switching function is constructed at fi tost by developing Lagrange's Interpolating formula into polynomial forms and then the constructing theory for two variables is driveloped. With these developed theory, multitle-variable Galois switching functions are constructed. Some examples for illustrating the theory are adopted from the existing papers and the results quite agree with the ones in the other papers.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.517-543
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• 2017

Let H be a cocommutative faithfully flat Hopf quasigroup in a strict symmetric monoidal category with equalizers. In this paper we introduce the notion of (strong) Galois H-object and we prove that the set of isomorphism classes of (strong) Galois H-objects is a (group) monoid which coincides, in the Hopf algebra setting, with the Galois group of H-Galois objects introduced by Chase and Sweedler.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.351-381
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• 2021

In this paper we introduce the notion of strong Galois H-progenerator object for a finite cocommutative Hopf quasigroup H in a symmetric monoidal category C. We prove that the set of isomorphism classes of strong Galois H-progenerator objects is a subgroup of the group of strong Galois H-objects introduced in [3]. Moreover, we show that strong Galois H-progenerator objects are preserved by strong symmetric monoidal functors and, as a consequence, we obtain an exact sequence involving the associated Galois groups. Finally, to the previous functors, if H is finite, we find exact sequences of Picard groups related with invertible left H-(quasi)modules and an isomorphism Pic(HMod) ≅ Pic(C)⊕G(H∗) where Pic(HMod) is the Picard group of the category of left H-modules, Pic(C) the Picard group of C, and G(H∗) the group of group-like morphisms of the dual of H.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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• pp.309-319
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• 2018

Galois polynomials are defined as a generalization of the cyclotomic polynomials. The definition of Galois polynomials (and cyclotomic polynomials) is based on the multiplicative group of integers modulo n, i.e. ${\mathbb{Z}}_n^*$. In this paper, we define Galois polynomials which are based on the quotient group ${\mathbb{Z}}_n^*/H$.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.85-94
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• 2006

We review Galois rings and permutation polynomials over Galois rings with emphasis on cryptological properties of Dickson polynomials and conclude that it is not plausible to obtain the Dickson scheme which has a Galois ring as a plaintext space.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.259-265
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• 2017

Galois polynomials are defined as a generalization of the Cyclotomic polynomials. Galois polynomials have integer coefficients as the cyclotomic polynomials. But they are not always irreducible. In this paper, Galois polynomials are partly classified according to the type of subgroups which defines the Galois polynomial.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.269-280
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• 2018

We study self-dual codes over Galois rings using the building-up construction method. In the construction, the existence of an antiorthogonal matrix is very important. In this study, we examine the existence problem of an antiorthogonal matrix over Galois rings.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.751-764
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• 2016

We investigate the self-dual codes over Galois rings and determine the mass formula for self-dual codes over Galois rings $GR(p^2,2)$.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.101-116
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• 2013

In this paper, we investigate the properties of fuzzy Galois (dual Galois, residuated, dual residuated) connections in a complete residuated lattice L.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.2
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• pp.129-134
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• 2011

We investigate the properties of Galois, dual Galois, residuated, and dual residuated connections on posets. In particular, we show that their connections are related to relations.