• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.1053-1054
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• 2006

In this paper we consider a family {$H_m$},m =1,2,..., of generalized Hadamard matrices of order $P^m$, where p is a prime number, and construct the corresponding family {$C^*_m$} of generalize p-ary Hadarmard codes which meet the Plotkin bound. Index terms: Cyclotomic fields, cocyclic matrices, Butson-Hadamard matrices, generalized Hadamard codes, decoding.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.3A
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• pp.412-416
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• 2000

Hadamard matrices are known to be important in designing of the orthogonal codes. in this paper we propose generalized Sylvester construction for Hadamard matrices. We prove it and give an example for the case of Hadamard matrices of order16.

• Journal of Communications and Networks
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• v.3 no.4
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• pp.361-364
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• 2001

Over an additive abelian group G of order g and for a given positive integer $\lambda$, a generalized Hadamard matrix GH(g, $\lambda$) is defined as a gλ$\times$gλ matrix[h(i, j)], where 1 $\leq i \leqg\lambda and 1 \leqj \leqg\lambda$, such that every element of G appears exactly $\lambd$atimes in the list h($i_1, 1) -h(i_2, 1), h(i_1, 2)-h(i_2, 2), …, h(i_1, g\lambda) -h(i_2, g\lambda), for any i_1\neqi_2$. In this paper, we propose a new method of expanding a GH(g^m, \lambda_1) = B = [B_{ij}] over G^m$ by replacing each of its m-tuple B_{ij} with B_{ij} + GH(g, $\lambda_2) where m = g\lambda_2. We may use g^m/\lambda_1 (not necessarily all distinct) GH(g, \lambda_2$)s for the substitution and the resulting matrix is defined over the group of order g.

• 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.

• 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.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.641-649
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• 2017

For partitioned matrices, the Khatri-Rao product is viewed as a generalized Hadamard product. In this paper we present Oppenheim's and Schur's determinantal inequalities for the Khatri-Rao product of two positive semidefinite matrices.

• 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.

• 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.