• Journal of the Institute of Electronics Engineers of Korea SD
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• v.48 no.8
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• pp.5-9
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• 2011

Spectral-amplitude-coding optical CDMA systems using codes based upon Hadamard matrices have very restrictive code lengths of $2^n$ and high phase-induced intensity noise(PIIN). In this paper a new code family, namely modified Hadamard code, is proposed to relax the code length restriction and the number of simultaneous users. The improved performance of the proposed system is analysed with the consideration of noise.

• Proceedings of the KIEE Conference
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• 1997.07b
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• pp.616-619
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• 1997

The spectrum-recovery scheme in Hadamard transform spectroscopy is commonly implemented with a fast Hadamard transform (FHT). When the Hadamard or simplex matrix corresponding to the mask does not have the same ordering as the Hadamard matrix corresponding to the FHT, a modification is required. When the two Hadamard matrices are in the same equivalence class, this modification can be implemented as a permutation scheme. This paper investigates permutation schemes for this application. This paper is to relieve the confusion about the applicability of existing techniques, reveals a new, more efficient method: and leads to an extension that allows a permutation scheme to be applied to any Hadamard or simplex matrix in the appropriate equivalence class.

• The Journal of the Korea institute of electronic communication sciences
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• v.9 no.4
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• pp.403-408
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• 2014

In this paper, we consider the encoding scheme of low density codes. In particular, we propose the fast encoding algorithm of the low density codes using circulant permutation matrices, The fast encoding algorithm is similar to the fast Hadamard transform, and the results show that the proposed scheme is a simple and fast encoding algorithm of the low density codes.

• Journal of Communications and Networks
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• v.12 no.3
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• pp.240-245
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• 2010

Jacket matrices, motivated by the complex Hadamard matrix, have played important roles in signal processing, communications, image compression, cryptography, etc. In this paper, we suggest a novel approach to design a simple class of space-time block codes (STBCs) to reduce its peak-to-average power ratio. The proposed code provides coding gain due to the characteristics of the complex Hadamard matrix, which is a special case of Jacket matrices. Also, it can achieve full rate and full diversity with the simple decoding. Simulations show the good performance of the proposed codes in terms of symbol error rate. For generality, a kind of quasi-orthogonal STBC may be similarly designed with the improved performance.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.10A
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• pp.1560-1565
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• 2000

Over an additive abelian group G of order g and for a given positive integer λ, a generalized Hadamard matrix GF(g,λ) is defined as a gλ$\times$gλ matrix [h(i,j)] where 1$\leq$i$\leq$gλ,1$\leq$j$\leq$gλ, such that every element of G appears exactly λ times in the list h(i$_1$,1)-h(i$_2$,1), h(i$_1$,2)-h(i$_2$,2),...,h(i$_1$,gλ)-h(i$_2$, gλ) for any i$\neq$j. In this paper, we propose a new method of expanding a GH(\ulcorner,λ$_1$) = B = \ulcorner over G by replacing each of its m-tuple \ulcorner with \ulcorner GH(g,λ$_2$) where m=gλ$_2$. We may use \ulcornerλ$_1$(not necessarily all distinct) GH(g,λ$_2$)'s for the substitution and the resulting matrix is defined over the group of order g.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.99-112
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• 2020

The study is about the bounds of the spectral norms of r-circulant and geometric circulant matrices with the sequences called biperiodic Jacobsthal numbers. Then we give bounds for the spectral norms of Kronecker and Hadamard products of these r-circulant matrices and geometric circulant matrices. The eigenvalues and determinant of r-circulant matrices with the bi-periodic Jacobsthal numbers are obtained.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.7
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• pp.19-26
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• 2013

In this paper we prove that all Jacket matrices are circulant and up to equivalence. This result leads to new constructions of Toeplitz Jacket(TJ) matrices. We present the construction schemes of Toeplitz Jacket matrices and the examples of $4{\times}4$ and $8{\times}8$ Toeplitz Jacket matrices. As a corollary we show that a Toeplitz real Hadamard matrix is either circulant or negacyclic.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.6
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• pp.319-327
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• 2016

In this paper we investigate that most of plants and animals have the symmetric property, such as a tree or a sheep's horn. In addition, the human body is also symmetric and contains the DNA. We can see the logarithm helices in Fibonacci series and animals, and helices of plants. The sunflower has a shape of circle. A circle is circular symmetric because the shapes are same when it is shifted on the center. Einstein's spatial relativity is the relation of time and space conversion by the symmetrically generalization of time and space conversion over the spacial. The left and right helices of plants and animals are the symmetric and have element-wise inverse relationships each other. The weight of center weight Hadamard matrix is 2 and is same as the base 2 of natural logarithm. The helix matrices are symmetric and have element-wise inverses.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.3
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• pp.25-33
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• 2015

As a reversible Jacket is having the compatibility of two sided wearing, the matrix that both the inside and the outside are compatible is called Jacket matrix, and the matrix is having both inside and outside by the processes of element-wise inverse and block-wise inverse. This concept had been completed by one of the authors Moon Ho Lee in 1989, and finally that resultant matrix has been christened as Jacket matrix, in 2000. This is the most generalized extension of the well known Hadamard matrices, which includes both orthogonal and non-orthogonal matrices. This matrix addresses many problems in information and communication theories. we investigate the properties of the Jacket matrix, i.e. determinants, eigenvalues, and kronecker product. These computations are very useful for signal processing and orthogonal codes design. In our proposal, we provide some results to calculate these values by using a very simple mathematical model with less complexity.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.841-849
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• 1997

A square matrix A with $per A \neq 0$ is called convertible if there exists a {1, -1} matrix H such that $per A = det(H \circ A)$ where $H \circ A$ denote the Hadamard product of H and A. In this paper, ranks of convertible {0, 1} matrices are investigated and the existence of maximal convertible matrices with its rank r for each integer r with $\left\lceil \frac{n}{2} \right\rceil \leq r \leq n$ is proved.