• The Journal of the Korea institute of electronic communication sciences
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• v.16 no.3
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• pp.533-540
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• 2021

To evaluate the performance of a system, one-dimensional 3-neighborhood cellular automata(CA) based pseudo-random generators are widely used in many fields. Although two-dimensional CA and one-dimensional 5-neighborhood CA have been applied for more effective key sequence generation, designing symmetric one-dimensional 5-neighborhood CA corresponding to a given primitive polynomial is a very challenging problem. To solve this problem, studies on one-dimensional 5-neighborhood CA synthesis, such as synthesis method using recurrence relation of characteristic polynomials and synthesis method using Krylov matrix, were conducted. However, there was still a problem with solving nonlinear equations. To solve this problem, a symmetric one-dimensional 5-neighborhood CA synthesis method using a transition matrix of 90/150 CA and a block matrix has recently been proposed. In this paper, we detail the theoretical process of the proposed algorithm and use it to obtain symmetric one-dimensional 5-neighborhood CA corresponding to high-order primitive polynomials.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.6
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• pp.117-123
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• 2014

This paper proposes the constructing method of effective multiplier using basis transformation. Th proposed multiplier is composed of the standard-dual basis transformation circuit module to change one input into dual basis the operation module to generate from bm to bm+k by the m degree irreducible polynomial, and the polynomial multiplicative module to consist of $m^2$ AND and m(m-1) EX-OR gates. Also, the dual-standard basis transformation circuit module to change the output part to be shown as a dual basis into standard basis is composed. The operation modules to need in each operational part are defined.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.2
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• pp.70-75
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• 2016

This paper proposes the constructing method of effective multiplier based on the finite fields in case of P=2. The proposed multiplier is constructed by polynomial arithmetic part, mod F(${\alpha}$) part and modular arithmetic part. Also, each arithmetic parts can extend according to m because of it have modular structure, and it is adopted VLSI because of use AND gate and XOR gate only. The proposed multiplier is more compact, regularity, normalization and extensibility compare with earlier multiplier. Also, it is able to apply several fields in recent hot issue IoT configuration.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.1-22
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• 2023

Let L(s, χ) be the Dirichlet L-series associated with an f-periodic complex function χ. Let P(X) ∈ ℂ[X]. We give an expression for ∑^f_n=1 χ(n)P(n) as a linear combination of the L(-n, χ)'s for 0 ≤ n < deg P(X). We deduce some consequences pertaining to the Chowla hypothesis implying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date no extended numerical computation on this hypothesis is available. In fact by a result of R. C. Baker and H. L. Montgomery we know that it does not hold for almost all fundamental discriminants. Our present numerical computation shows that surprisingly it holds true for at least 65% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. We also show that a generalized Chowla hypothesis holds true for at least 72% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. Since checking this generalized Chowla's hypothesis is easy to program and relies only on exact computation with rational integers, we do think that it should be part of any numerical computation verifying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date, this verification for real, even and primitive Dirichlet characters has been done only for conductors less than 2·10⁵.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.3
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• pp.60-68
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• 1994

In this paper, the multiplicative algorithm of two polynomials over finite field GF(($p^{m}$) is presented. Using the presented algorithm, the multiple-valued multiplier of the serial input-output modular structure by CCD is constructed. This multiple-valued multiplier on CCD is consisted of three operation units: the multiplicative operation unit, the modular operation unit, and the primitive irreducible polynomial operation unit. The multiplicative operation unit and the primitive irreducible operation unit are composed of the overflow gate, the inhibit gate and mod(p) adder on CCD. The modular operation unit is constructed by two mod(p) adders which are composed of the addition gate, overflow gate and the inhibit gate on CCD. The multiple-valued multiplier on CCD presented here, is simple and regular for wire routing and possesses the property of modularity. Also. it is expansible for the multiplication of two elements on finite field increasing the degree mand suitable for VLSI implementation.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1711-1723
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• 2013

P. V$\acute{a}$mos called a ring R 2-good if every element is the sum of two units. The ring of all $n{\times}n$ matrices over an elementary divisor ring is 2-good. A (right) self-injective von Neumann regular ring is 2-good provided it has no 2-torsion. Some of the earlier results known to us about 2-good rings (although nobody so called at those times) were due to Ehrlich, Henriksen, Fisher, Snider, Rapharl and Badawi. We continue in this paper the study of 2-good rings by several authors. We give some examples of 2-good rings and their related properties. In particular, it is shown that if R is an exchange ring with Artinian primitive factors and 2 is a unit in R, then R is 2-good. We also investigate various kinds of extensions of 2-good rings, including the polynomial extension, Nagata extension and Dorroh extension.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.47-52
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• 2018

Let ${\delta}$ be a derivation in a noetherian integral domain A. It is shown that a natural map induces a homeomorphism between the spectrum of $A[z;{\delta}]$ and the Poisson spectrum of $A[z;{\delta}]_p$ such that its restriction to the primitive spectrum of $A[z;{\delta}]$ is also a homeomorphism onto the Poisson primitive spectrum of $A[z;{\delta}]_p$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.10A
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• pp.1576-1581
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• 2000

We investigated into the minimum distance of a primitive binary cyclic code C with a generator polynomial g(x)=$m_1(x)m_{d}(x)$. It is known that the necessary and sufficient condition for C to have minimum distance five is the fact that \ulcorner is an APN power function. In this paper we derived the new proof of minimum distance for the primitive binary cyclic codes with minimum distance five.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2006.05a
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• pp.393-396
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• 2006

In this paper, we analyze the characteristic polynomials of 90/150 cellular automata which uses only 90, 150 rules as state-transition rules. In particular, we propose the method which the characteristic polynomial is represented as the exponential type of a primitive polynomial by synthesizing 90/150 CA.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.05a
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• pp.433-436
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• 2009

Many researchers had made a diversity of attempts for generating pseudorandom sequences such as the method of using LFSR whose characteristic polynomial is a primitive polynomial, of using Cellular Automata and of using quadratic functions. In this paper, we can analyze and characterize the methods for generating maximal period pseudorandom sequences constructed by quadratic functions.