• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.7C
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• pp.635-639
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• 2009

In this paper, we show that any two Hadamard matrices of the same size are equivalent if they have the property that the rows of each Hadamard matrix are closed under binary vector addition. One of direct consequences of this result is that the equivalence between cyclic Hadamard matrices constructed by maximal length sequences and Walsh-Hadamard matrix of the same size generated by Kronecker product can be established.

• 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.

• 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 the Korean Mathematical Society
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• v.32 no.2
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• pp.351-361
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• 1995

Let M be a complete open Riemannian manifold. When the sectional curvature $K_M$ of M is nonpositive, Gromov has defined, in his lectures [3], the ideal boundary of M, and used it to study the geometric structure of M. In a Hadamard manifold, a simply connected manifold with nonpositive sectional curvature, a point at infinity can be defined as an equivalence class of rays. He proved many interesting theorems using this definition of ideal boundary and the so-called Tit's metric on it. He also suggested a counterpart to this for nonnegative curvature case. This idea has been taken up by Kasue to study the structure of complete open manifolds with asympttically nonnegative curvature [14]. Motivated by these works, we will define an idela boundary of a general noncompact manifold M, and study its structure.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.8C
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• pp.1069-1075
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• 2004

In this paper, we show the equivalence between complementary code keying (CCK) codeword and coset of the first order Reed-Muller (RM) code with variables of three. The CCK codewords are Golay sequences which have peak-to-average power ratio (PAPR) of two at most and can correct one error. We propose a CCK-orthogonal frequency division multiplexing (OFDM) modem to reduce PAPR. Also, we present the performance improvement techniques by increasing the variables of four to correct three errors and reduce PAPR at least 9㏈ with this system. Although, two Fast Hadamard Transform (FHT) blocks of size 8 64 are required at the receiver, we reduce the complexity by using FHT blocks of size 8 64 and 2 4 without deteriorating the performance. We generalize our results that we may increase the variables of RM code to enhance the error correcting and PAPR reduction capabilities without increasing receiver's complexity.