• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권3호
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• pp.1193-1209
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• 2015

Network coding is promising to maximize network throughput and improve the resilience to random network failures in various networking systems. In this paper, the problem of providing efficient confidentiality for practical network coding system against a global eavesdropper (with full eavesdropping capabilities to the network) is considered. By exploiting a novel combination between the construction technique of systematic Maximum Distance Separable (MDS) erasure coding and traditional cryptographic approach, two efficient schemes are proposed that can achieve the maximum possible rate and minimum encryption overhead respectively on top of any communication network or underlying linear network code. Every generation is first subjected to an encoding by a particular matrix generated by two (or three) Vandermonde matrices, and then parts of coded vectors (or secret symbols) are encrypted before transmitting. The proposed schemes are characterized by tunable and measurable degrees of security and also shown to be of low overhead in computation and bandwidth.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권2호
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• pp.3-8
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• 2007

In this paper a generalized parametric mean length $L(P^{\nu},\;R)$ has been defined and bounds for $L(P^{\nu},\;R)$ are obtained in terms of generalized R-norm information measure.

• 대한수학회지
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• 제51권5호
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• pp.941-953
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• 2014

In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and obtain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제33권3호
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• pp.163-180
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• 2019

본 연구에서는 다양한 배경을 가진 대학 신입생들이 단기간에 미적분학의 주요 개념을 이해할 수 있도록 돕고, 현실에서 접하는 복잡한 문제들에 대한 문제해결력도 기르면서, 동시에 컴퓨팅 사고력도 신장시킬 수 있는 미적분학 교수 학습에 대하여 논한다. 구체적인 방안으로, 본 연구진은 '파이썬(Python) 기반의 코딩(coding)교육을 적용한 대학 미적분학의 교수 학습' 콘텐츠를 개발하고 실제 수업 현장에 적용하여 유의미한 성과를 거둔 사례를 보고한다. 즉, 파이썬 언어 기반의 코딩교육을 적용한 미적분학 I, II의 구체적인 교수 학습 설계, 실천 계획안 그리고 평가라는 전 과정이 실제로 진행된 사례와 그에 활용된 자료들을 정리하여 공유한다. 개발된 교안과 코드 및 사이버 실습실은 언제 어디서나 무료로 활용할 수 있으며, 교수자와 학생은 공유된 콘텐츠와 학생활동 기록을 참고하며, 자유롭게 미적분학을 교수 학습하고, 주어진 코드를 활용하여 실습하면서 미적분학의 직관적인 이해를 높임과 동시에 컴퓨팅 사고력도 신장시킬 수 있도록 하였다. 또한 교수자는 학생들의 질의 응답 참여, 보고서 발표, 팀워크 등이 포함된 플립드러닝(flipped learning)과 과정중심의 모든 데이터를 기반하여 평가함으로써 학생들의 미적분학 지식에 대한 상향평준화를 돕게 된다. 본 연구에서 제시한 대학 미적분학의 교수 학습 사례는 학생들이 미적분학 개념과 컴퓨팅 사고력을 동시에 신장시켜 사회가 필요로 하는 인재로 성장할 수 있도록 도울 수 있는 가능성을 보여주는 대학 수학 교육의 교수 학습 모델이 될 것으로 본다.

• Journal of Information Processing Systems
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• 제13권1호
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• pp.40-56
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• 2017

Since the progress of digital medical imaging techniques, it has been needed to compress the variety of medical images. In medical imaging, reversible compression of image's region of interest (ROI) which is diagnostically relevant is considered essential. Then, improving the global compression rate of the image can also be obtained by separately coding the ROI part and the remaining image (called background). For this purpose, the present work proposes an efficient reversible discrete cosine transform (RDCT) based embedded image coder designed for lossless ROI coding in very high compression ratio. Motivated by the wavelet structure of DCT, the proposed rearranged structure is well coupled with a lossless embedded zerotree wavelet coder (LEZW), while the background is highly compressed using the set partitioning in hierarchical trees (SPIHT) technique. Results coding shows that the performance of the proposed new coder is much superior to that of various state-of-art still image compression methods.

• 대한수학회보
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• 제55권6호
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• pp.1627-1638
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• 2018

In this paper, we study an special type of cyclic codes called skew cyclic codes over the ring ${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$, where p is a prime number. This set of codes are the result of module (or ring) structure of the skew polynomial ring (${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$)[$x;{\theta}$] where $v^3=1$ and ${\theta}$ is an ${\mathbb{F}}_p$-automorphism such that ${\theta}(v)=v^2$. We show that when n is even, these codes are either principal or generated by two elements. The generator and parity check matrix are proposed. Some examples of linear codes with optimum Hamming distance are also provided.

• 한국학교수학회논문집
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• 제5권2호
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• pp.23-31
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• 2002

The purpose of this study is to analyze thinking process in problem solving and to get some teaching materials to improve students' problem solving abilities. For this study, 14 girl and boy students in highschool were tested with 7 testing questions. The whole process of students' problem solving was observed by using 'Thinking aloud', recorded by Audio Tape and finally drawn up to Protocol. On the basis of that Protocol, coding system was set up and characteristics of thinking process in each stage were analyzed. -In the stage of planning, successful problem solvers tried to check the properties of words included in problems(Pr) and made it clear that they were seeking(O) -In the stage of planning, students used abstraction strategy(Ab, making equation(E) or using variable(V)) appropriately could solve more difficult problems. Successful problem solvers turned used unsystematical trial into systematical method and were good at using partial objects, assistant factors. - In the stage of carring out the plan, successful problem solvers to reduce the error, check the purpose, used formula, knowledge and calculation. -In the looking back stage, successful problem solvers generalized the answer and checked the total process.

• 인터넷정보학회논문지
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• 제24권1호
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• pp.27-37
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• 2023

본 논문에서는 파도반 수열을 이용하여 새로운 루카스-파도반(Lucas-Padovan) 수열을 정의하고, 이를 이용하여 새로운 위상적 상호연결 네트워크(Interconnection Networks)를 구축한다. 루카스-파도반 수열의 부분 수열을 이용하여 음이 아닌 정수를 코딩(Coding)하고, 이를 이용하여 루카스-파도반 큐브(Cubes)를 새롭게 구축하여 위상적 성질을 다룬다.

• 호남수학학술지
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• 제33권2호
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• pp.153-161
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• 2011

Greg([Greg]) considered that $$N_k= \sum\limits_{i=1}^k(-1)^{i+1}P_{i,k}(p)N_1^i$$ where the $P_{i,k}$'s were polynomials with positive integer coefficients. In this paper, we will give the equations for $\sum\limits{P_{i,k}$ modulo 3. Using this, if we send a information for elliptic curve to sender, we can make a new checksum method for Manchester coding in IEEE 802.3 or IEEE 802.4.

• 충청수학회지
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• 제22권2호
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• pp.245-250
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• 2009

We consider a code function from the unit interval which has a generalized dyadic expansion into a coding space which has an associated ultra metric. The code function is not a bi-Lipschitz map but a dimension-preserving map in the sense that the Hausdorff and packing dimensions of any subset in the unit interval and its image under the code function coincide respectively.