• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.29-44
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• 2021

The set D of column vectors of a generator matrix of a linear code is called a defining set of the linear code. In this paper we consider the problem of constructing few-weight (mainly two- or three-weight) linear codes from defining sets. It can be easily seen that we obtain an one-weight code when we take a defining set to be the nonzero codewords of a linear code. Therefore we have to choose a defining set from a non-linear code to obtain two- or three-weight codes, and we face the problem that the constructed code contains many weights. To overcome this difficulty, we employ the linear codes of the following form: Let D be a subset of ��2n, and W (resp. V ) be a subspace of ��2 (resp. ��2n). We define the linear code ��D(W; V ) with defining set D and restricted to W, V by $${\mathcal{C}}_D(W;V )=\{(s+u{\cdot}x)_{x{\in}D^{\ast}}|s{\in}W,u{\in}V\}$$. We obtain two- or three-weight codes by taking D to be a Vasil'ev code of length n = 2m - 1(m ≥ 3) and a suitable choices of W. We do the same job for D being the complement of a Vasil'ev code. The constructed few-weight codes share some nice properties. Some of them are optimal in the sense that they attain either the Griesmer bound or the Grey-Rankin bound. Most of them are minimal codes which, in turn, have an application in secret sharing schemes. Finally we obtain an infinite family of minimal codes for which the sufficient condition of Ashikhmin and Barg does not hold.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1259-1265
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• 2016

In this paper, we introduce the notions of mean open and closed sets in topological spaces, and obtain some properties of such sets. We observe that proper paraopen and paraclosed sets are identical to mean open and closed sets respectively.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.329-336
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• 2004

In this paper, we study relationships between zero characteristic properties and minimality of orbit closures or limit sets of points. Also, we characterize the set of points of zero characteristic properties. We show that the set of points of positive zero characteristic property in a compact spaces X is the intersection of negatively invariant open subsets of X.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.103-111
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• 1999

In this paper, we introduce a generalized regular homomorphism as the extending notion of the regular homomorphism.

• Journal of KIISE:Information Networking
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• v.34 no.3
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• pp.226-238
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• 2007

In this paper, we present a novel fully distributed topology control protocol that can construct the multiple-ring topology of Minimal Connected Dominating Set (MCDS) as the transport backbone for mobile ad hoc networks. It makes a topology from the minimal nodes that are chosen from all the nodes, and the constructed topology is comprised of the minimal physical links while preserving connectivity. This topology reduces the interference. The all nodes work as the nodes of the distributed parallel Boltzmann machine, of which the objective function is consisted of two Boltzmann factors: the link degree and the connection domination degree. To define these Boltzmann factors, we extend the Connected Dominating Set into a fuzzy set, and also define the fuzzy set of nodes by which the multiple-ring topology can be constructed. To construct the transport backbone of the mobile ad hoc network, the proposed protocol chooses the nodes that are the strong members of these two fuzzy sets as the clusterheads. We also ran simulations to provide the quantitative comparison against the related works in terms of the packet loss rate and the energy consumption rate. As a result, we show that the network that is constructed by the proposed protocol has far better than the other ones with respect to the packet loss rate and the energy consumption rate.

• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.1-5
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• 2018

It is proved that 'maximum' is actually attained in the following risk measure representation $${\rho}_m(X)={max \atop Q{\in}Q_m}E_Q[-X]$$.

• Journal of the Korean Society of Safety
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• v.36 no.4
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• pp.12-19
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• 2021

This paper presents a safety assessment method for FTA-based induction heating systems; the failures and causes of electrical fire are first analyzed for each part and module qualitatively, and methods to manage high probabilities of failure and electrical fire are considered, thereby improving the reliability of the induction heating system. The cumulative importance value (ACC) of the minimal cut set is drawn by setting failure as the top event, and STACK and SMPS are observed to account for about 70% of the induction heating system failures. Thus, intensively managing the basic events contained in the minimal cut set of failures for STACK and SMPS is expected to provide effective and stable operation of the induction heating system. When electrical fire is set as the top event, the STACK percentage is 90%. Accordingly, the current IGBT is changed to a FET to increase the applied voltage and prevent induction heating system failure, and a heat sink plane is installed to prevent FET heating caused by switching, thereby preventing an electrical fire. By classifying the parts and modules of the induction heating system in detail and by applying FTA based on actual failure rates and relevant data, more practical and reasonable results may be expected. Hence, continuous research must be conducted to ensure safety when using induction heating systems.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.5
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• pp.379-389
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• 1988

In this paper, an algorithm for obtaining 2-state switching failure function and a terminal pair reliability evaluation method in a communication network are proposed. The communication network is modeled by a graph. By using the sequence of matrix transformations for the graph, minimal cut-set matrix representing all minimal cut-sets which completely interrupt the communication path is determined and 2-state switching failure function is then obtained from the minimal cut-set matrix. The terminal pari reliability of the communication network is evaluated by corresponding the random variables to 2-state switching failure function. Illustrative examples are provided to demonstrate the algorithm. A computer program evaluating the terminal pair reliability in a complex and large network has also been developed.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.883-902
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• 2008

The main results concern with the self maps on the Klein bottle. We obtain the Reidemeister numbers and the Nielsen numbers for all self maps on the Klein bottle. In terms of the Nielsen numbers of their iterates, we totally determine the minimal sets of periods for all homotopy classes of self maps on the Klein bottle.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.264-267
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• 1991

In this paper, a new application method of the Kalman filter to desigin a gyro is proposed. The role of a gyro is the estimation of an input rate with minimal error covariance. The size of the error covariance depends on gyro's parameters, which makes it possible to use the parameters of gyro to minimze the estimation error covariance. Numerical analysis shows that the error covariance becomes smaller as the spin axis momentum becomes larger and the damping coefficient smaller, but production cost must be considered. Through numerical analysis the parameter set for an acceptable - performance gyro with small cost can be selected.