• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.193-204
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• 2022

We present construction methods for free self-orthogonal (self-dual or Type II) codes over ℤ₄[v]/〈v² + 2v〉 which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on ℤ₄, we give a construct method for a code over ℤ₄. We have some new and optimal codes over ℤ₄ with respect to the minimum Lee weight or minimum Euclidean weight.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.725-742
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• 2014

In this paper, we find all inequivalent classes of self-orthogonal codes over $Z_{p^2}$ of lengths $l{\leq}3$ for all primes p, using similar method as in [3]. We find that the classification of self-orthogonal codes over $Z_{p^2}$ includes the classification of all codes over $Z_p$. Consequently, we classify all the codes over $Z_p$ and self-orthogonal codes over $Z_{p^2}$ of lengths $l{\leq}3$ according to the automorphism group of each code.

• Korean Management Science Review
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• v.21 no.2
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• pp.43-60
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• 2004

Every iteration of interior-point methods of large scale optimization requires computing at least one orthogonal projection. In the practice, symmetric variants of the Gaussian elimination such as Cholesky factorization are accepted as the most efficient and sufficiently stable method. In this paper several specific implementation issues of the symmetric factorization that can be applied for solving such equations are discussed. The code called McSML being the result of this work is shown to produce comparably sparse factors as another implementations in the $MATLAB^{***}$ environment. It has been used for computing projections in an efficient implementation of self-regular based interior-point methods, McIPM. Although primary aim of developing McSML was to embed it into an interior-point methods optimizer, the code may equally well be used to solve general large sparse systems arising in different applications.

• International Journal of Computer Science & Network Security
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• v.22 no.11
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• pp.241-247
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• 2022

Ad hoc network is self-organized network powered by battery. The reliability of virtual user identification and channel security are reduced when SNR is low due to limited user energy. In order to solve this problem, a joint virtual user identification and channel security en/decoding method is proposed in this paper. Transmitter-receiver-based virtual user identification code is generated by executing XOR operation between orthogonal address code of transmitter and pseudo random address code of receiver and encrypted by channel security code to acquire orthogonal random security sequence so as to improve channel security. In order to spread spectrum as well as improve transmission efficiency, data packet is divided into 6-bit symbols, each symbol is mapped with an orthogonal random security sequence. Subspace-based method is adopted by receiver to process received signal firstly, and then a judgment model is established to identify virtual users according to the previous processing results. Simulation results indicate that the proposed method obtains 1.6dB E_b/N₀ gains compared with reference methods when miss alarm rate reaches 10^-3.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.965-989
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• 2015

Let p, ${\ell}$ be distinct odd primes, q be an odd prime power with gcd(q, p) = gcd(q,${\ell}$) = 1, and m, n be positive integers. In this paper, we determine all self-dual, self-orthogonal and complementary-dual negacyclic codes of length $2p^{n{\ell}m}$ over the finite field ${\mathbb{F}}_q$ with q elements. We also illustrate our results with some examples.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.289-317
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• 2002

We associate binary codes to polynomials over fields of characteristic two and show that the binary Golay codes are associated to the Mathieu group polynomials in characteristics two. We give two more polynomials whose Galois group in $M_{12}$ but different self-orthogonal binary codes are associated. Also, we find a family of $M_{24}$-coverings which includes previous ones.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2002.11a
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• pp.159-162
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• 2002

데이터에 삽입되어 있는 워터마크를 제거하려는 공격기법이 점차 발전되면서 여러 가지 워터마킹 알고리즘이 등장하게 된다. 보통 워터마크를 제거하기 위해서는 워터마크 신호의 동기를 제거하는 동기-제거(De-Syncronization) 공격 방법을 이용한다. 이런 공격에 대처하기 위한 워터마킹 방법으로는 세 가지로 분류할 수 있는데, 공격에 영향을 받지 않는 영역(invariant domain)에 워터마크를 삽입하는 방법, 템플릿(template)을 이용한 방법, 자기 참조(self-reference)를 이용한 기법 등이 있다. 본 논문에서는 공간 영역에서의 자기 참조 워터마킹 방법을 소개하고, 이에 적합한 메시지를 삽입하고 검출하는 방법에 대해 제안한다. 삽입하려는 메시지와 Reed-solomon Code를 이용하여 만든 부가적인 정보를 QOS(Quasi-orthogonal sequences)방법과 DSSS를 이용하여 만든 다음 키 값을 이용하여 뒤섞으면 워터마킹 블록을 자기 참조 워터마킹 방법으로 영상에 삽입하게 된다. 그 결과 일반적 필터링 공격에는 95% 이상 검출됐고, JPEG 압축 파라미터 60에서도 97% 이상 검출되었다.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.11
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• pp.943-950
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• 2013

This paper discusses a harmonic response estimation method on the L$\acute{e}$vy plate with two opposite edges simply supported and the other two edges having free boundary conditions. Since the equation of motion of the plate is not self-adjoint, the modes are not orthogonal to each other on the domain. Noting that the L$\acute{e}$vy plate can be expressed using one term sinusoidal function that is orthogonal to other sinusoidal functions, this paper suggested the calculation method that is equivalent to finding a least square error minimization solution of the finite number of algebraic equations. Example problems subjected to a distributed area loading and a distributed line loading are defined and their solutions are provided. The solutions are compared to those of the commercial code, ANSYS. According to the verification results, it is expected that the suggested method will be useful to predict the forced response on the L$\acute{e}$vy plate with the distributed area or line loading conditions.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.131-150
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• 2019

In this paper, we consider the structure of ${\gamma}$-constacyclic codes of length $2p^s$ over the Galois ring $GR(p^a,m)$ for any unit ${\gamma}$ of the form ${\xi}_0+p{\xi}_1+p^2z$, where $z{\in}GR(p^a,m)$ and ${\xi}_0$, ${\xi}_1$ are nonzero elements of the set ${\mathcal{T}}(p,m)$. Here ${\mathcal{T}}(p,m)$ denotes a complete set of representatives of the cosets ${\frac{GR(p^a,m)}{pGR(p^a,m)}}={\mathbb{F}}p^m$ in $GR(p^a,m)$. When ${\gamma}$ is not a square, the rings ${\mathcal{R}}_p(a,m,{\gamma})=\frac{GR(p^a,m)[x]}{{\langle}x^2p^s-{\gamma}{\rangle}}$ is a chain ring with maximal ideal ${\langle}x^2-{\delta}{\rangle}$, where ${\delta}p^s={\xi}_0$, and the number of codewords of ${\gamma}$-constacyclic code are provided. Furthermore, the self-orthogonal and self-dual ${\gamma}$-constacyclic codes of length $2p^s$ over $GR(p^a,m)$ are also established. Finally, we determine the Rosenbloom-Tsfasman (RT) distances and weight distributions of all such codes.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.17 no.7 s.110
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• pp.638-647
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• 2006

Recently, the DFT-Spread OFDM has been studied for the PAPR reduction. However, the DFT-Spread OFDM produces more ICI and SCI problems than OFDM because phase offset mismatch of the DFT spreading code results from the random phase noise in the oscillator. In this paper, at first, phase noise influence on the DFT-Spread OFDM system is theoretically analyzed in terms of the BER performance. Then, the conventional ICI self-cancellation methods are discussed and two kinds of ICI self-cancellation methods are newly proposed. Lastly, a new DFT-Spread OFDM system which selectively adopts the ICI self-cancellation technique is proposed to resolve the interference problem and PAPR reduction simultaneously. Proposednew DFT-Spread OFDM system can minimize performance degradation caused by phase noise, and still maintain the low PAPR property. Among the studied methods, DFT-Spread OFDM with data-conjugate method or newly proposed symmetric data-conjugate method show the significant performance improvements, compared with the DFT-Spread OFDM without ICI self-cancellation schemes. The data-conjugate method is slightly better than symmetric data-conjugate method.