• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1129-1147
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• 2021

This paper aims to analyze the PTG module for the finite-dimensional odd Contact superalgebra over a field of prime characteristic by using the method of Hu and Shen's mixed product realization. The general acting law in odd Contact superalgebra is obtained. In addition, the structure and irreducibility of graded module for odd Contact superalgebra are discussed.

• East Asian mathematical journal
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• v.30 no.3
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• pp.321-326
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• 2014

In this paper, we present a simple proof of Corollary 3.3 in [5] using the fact that for a K3 surface of finite height over a field of odd characteristic, the height is a multiple of the non-symplectic order. Also we prove for a non-symplectic CM K3 surface defined over a number field the Frobenius invariant of the reduction over a finite field is determined by the congruence class of residue characteristic modulo the non-symplectic order of the K3 surface.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.287-295
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• 2014

In this paper, we prove that the image of the representation of the automorphism group of a supersingular K3 surface of Artin-invariant 1 over odd characteristic p on the global two forms is a finite cyclic group of order p + 1. Using this result, we deduce, for such a K3 surface, there exists an automorphism which cannot be lifted over a field of characteristic 0.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.159-168
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• 2003

In this paper we discuss the Construction Of 3 new extension field of characteristic odd and analyze the complexity of arithmetic operations over such a field. Also we show that it is suitable for Elliptic Curve Cryptosystems(ECC) and Digital Signature Algorithm(DSA, 〔7〕) as an underlying field. In particular, our digital signature scheme is at least twice as efficient as DSA.

• East Asian mathematical journal
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• v.35 no.5
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• pp.589-595
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• 2019

In this paper, we prove that a special supersingular K3 surface of Artin invariant ${\sigma}$ over a field of odd characteristic p has a model over a finite field of $p^{2{\sigma}}$ elements.

• Journal of information and communication convergence engineering
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• v.16 no.3
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• pp.166-172
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• 2018

A pseudo-random sequence generated by using a primitive polynomial, trace function, and Legendre symbol has been researched in our previous work. Our previous sequence has some interesting features such as period, autocorrelation, and linear complexity. A pseudo-random sequence widely used in cryptography. However, from the aspect of the practical use in cryptographic systems sequence needs to generate swiftly. Our previous sequence generated by utilizing a primitive polynomial, however, finding a primitive polynomial requires high calculating cost when the degree or the characteristic is large. It’s a shortcoming of our previous work. The main contribution of this work is to find some relation between the generated sequence and irreducible polynomials. The purpose of this relationship is to generate the same sequence without utilizing a primitive polynomial. From the experimental observation, it is found that there are (p - 1)/2 kinds of polynomial, which generates the same sequence. In addition, some of these polynomials are non-primitive polynomial. In this paper, these relationships between the sequence and the polynomials are shown by some examples. Furthermore, these relationships are proven theoretically also.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.591-605
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• 2013

The underlying field is of characteristic $p$ > 2. In this paper, we first use the method of computing the homogeneous derivations to determine the first cohomology of the so-called odd contact Lie algebra with coefficients in the even part of the generalized Witt Lie superalgebra. In particular, we give a generating set for the Lie algebra under consideration. Finally, as an application, the derivation algebra and outer derivation algebra of the Lie algebra are completely determined.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.653-664
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• 2002

This article discusses a new representation of the generalized Fisher flocks and shows that there is a unique flock for each full field K of odd or zero characteristic that has a full field quadratic extension. It is also shown that partial flock extensions of 'critical linear subflocks'are completely determined.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.39-44
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• 1988

In 1940, B. H. Neumann, working with a system more general than a near-field, proved that the additive group of such a system (and of a near-field) is commutative. The algebraic structure he used is known as a Neumann system (N-system). Here, the prime N-systems are classified and for each possible characteristic, examples of N-systems which are neither near-fields nor rings are given. It is also shown that a necessary condition for the set of all odd polynomials over GF(p) to be an N-system is that p is a Fermat prime.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1025-1034
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• 2023

Let U be the restricted quantized enveloping algebra Ũ_q(𝖘𝖑₂) over an algebraically closed field of characteristic zero, where q is a primitive 𝑙-th root of unity (with 𝑙 being odd and greater than 1). In this paper we show that any indecomposable submodule of U under the adjoint action is generated by finitely many special elements. Using this result we describe all ideals of U. Moreover, we classify annihilator ideals of simple modules of U by generators.