• Journal of electromagnetic engineering and science
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• v.7 no.1
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• pp.17-27
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• 2007

Jacket matrices which are defined to be $n{\times}n$ matrices $A=(a_{jk})$ over a field F with the property $AA^+=nI_n$ where $A^+$ is the transpose matrix of elements inverse of A,i.e., $A^+=(a_{kj}^-)$, was introduced by Lee in 1984 and are used for signal processing and coding theory, which generalized the Hadamard matrices and Center Weighted Hadamard matrices. In this paper, some properties and constructions of Jacket matrices are extensively investigated and small orders of Jacket matrices are characterized, also present the full rate and the 1/2 code rate complex orthogonal space time code with full diversity.

• 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.

• Journal of electromagnetic engineering and science
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• v.7 no.1
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• pp.28-34
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• 2007

In this paper, we present a quasi-Jacket block matrices over binary matrices which all are belong to a class of cocyclic matrices is the same as the Hadamard case and are useful in digital signal processing, CDMA, and coded modulation. Based on circular permutation matrix(CPM) cocyclic quasi block low-density matrix is introduced in this paper which is useful in coding theory. Additionally, we show that the fast algorithm of quasi-Jacket block matrix.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.5
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• pp.9-17
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• 2013

In this paper we introduce modular symmetric designs and use them to study the existence of Hadamard-Jacket matrices modulo 3/5. We prove that there exist 5-modular Hadamard-Jacket matrices of order n if and only if n≢3.7 (mod 10) and n≢6,11. In particular, this solves the 5-modular version of the Hadamard conjecture.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.42 no.8 s.338
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• pp.1-10
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• 2005

In this paper, the explicit low density codes construction from the generalized permutation matrices related to algebra theory is investigated, and we design several Jacket inverse block matrices on the recursive formula and permutation matrices. The results show that the proposed scheme is a simple and fast way to obtain the low density codes, and we also Proved that the structured low density parity check (LDPC) codes, such as the $\pi-rotation$ LDPC codes are the low density Jacket inverse block matrices too.

• Journal of Communications and Networks
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• v.13 no.1
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• pp.12-16
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• 2011

In this paper, we construct two families $C^*_m$ and ${\~{C}}^*_m$ of ternary ($2^m$, $3^m$, $2^{m-1}$ ) and ($2^m$, $3^{m+1}$, $2^{m-1}$ ) codes, for m = 1, 2, 3, ${\cdots}$, derived from the corresponding families of modified ternary Jacket matrices. These codes are close to the Plotkin bound and have a very easy decoding procedure.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.3
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• pp.15-24
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• 2015

Jacket matrices which are defined to be $m{\times}m$ matrices $J^{\dagger}=[J_{ik}^{-1}]^T$ over a Galois field F with the property $JJ^{\dagger}=mI_m$, $J^{\dagger}$ is the transpose matrix of element-wise inverse of J, i.e., $J^{\dagger}=[J_{ik}^{-1}]^T$, were introduced by Lee in 1984 and are used for Digital Signal Processing and Coding theory. This paper presents some square matrices $A_2$ which can be eigenvalue decomposed by Jacket matrices. Specially, $A_2$ and its extension $A_3$ can be used for modifying the properties of hyperbola and hyperboloid, respectively. Specially, when the hyperbola has n times transformation, the final matrices $A_2^n$ can be easily calculated by employing the EVD[7] of matrices $A_2$. The ideas that we will develop here have applications in computer graphics and used in many important numerical algorithms.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.252-254
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• 2007

In this paper, we will introduce an encoding algorithm of LDPC Codes in Direct-Sequence UWB systems. We evaluate the performance of the coded systems in an AWGN channel. This new algorithm is based on the Jacket matrics. Mathematically let A = ($a_{kl}$) be a matnx, if $A^{-1}$ = $(a^{-1}_{kl})^r$,then the matrix A is a Jacket matrix. If the Jacket matrices if Low density, the inverse matrices is also Low density which is very important to the introduced encoding algorithm.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.11
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• pp.2512-2520
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• 1997

The classes of Reverse Jacket matrix [RJ]$_{N}$ and the corresponding Restclass Reverse Jacket matrix ([RRJ]$_{N}$) are defined;the main property of [RJ]$_{N}$ is that the inverse matrices of them can be obtained very easily and have a special structure. [RJ]$_{N}$ is derived from the weighted hadamard Transform corresponding to hadamard matrix [H]$_{N}$ and a basic symmertric matrix D. the classes of [RJ]$_{2}$ can be used as a generalize Quincunx subsampling matrix and serveral polygonal subsampling matrices. In this paper, we will present in particular the systematical block-wise extending-method for {RJ]$_{N}$. We have deduced a new orthorgonal matrix $M_{1}$.mem.[RRJ]$_{N}$ from a nonorthogonal matrix $M_{O}$.mem.[RJ]$_{N}$. These matrices can be used to develop efficient algorithms in IMT2000 signal processing, multidimensional subsampling, spectrum analyzers, and signal screamblers, as well as in speech and image signal processing.gnal processing.g.