• 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.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.3
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• pp.163-167
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• 2009

In this paper, we analyze key agreement algorithms based on co-cyclic Jacket matrices, and propose key agreement algorithms based on co-cyclic Hadamard matrices to fix the problem. The performance of our proposal is better than conventional one's and the construction of the matrices is very simple. Also time complexity of our proposal is proportional to the factor that determinees the size of the matrix, and the length of the key. So our proposal is fast and will be useful for the communcations of two or three users, especially for those have low computing power.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.12
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• pp.1527-1536
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• 1999

In this paper, a triply-encoded Hadamard transform imaging spectrometer is proposed by applying the grill spectrometer to the Hadamard transform imaging spectrometer. The proposed system encodes the input radiation triply ; once through the input image mask and twice through the two masks in the grill spectrometer. We use an electro-optical mask in the grill spectrometer which is controlled by a left-cyclic simplex matrix. Then we modeled the system using $D^{-1}$ method. In this paper, the average mean square error associated with a recovered estimate is considered for performance evaluation. The relative performance is compared with those of the other conventional systems.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.571-579
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• 1999

In this paper, a Hadamard transform imaging spectrometer(HTIS) is proposed by using a grill spectrometer. And we reconfigure the system by using the grill sectrometer which uses a left cyclic S-matrix instead of the conventional right cyclic one. Then, we model the Hadamard transform imaging spectrometer and apply the mask characteristics compensation method, i.e. $ {T}^{-1}$ method, to complete fast algorithm. Also, through computer simulations the superiority of the proposed system in this paper to the conventional Hadamard transform spectrometer(HTS) is proved and the performance of the two systems are compared by introducing average mean square error(AMSE) as the algebraic criterion.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.9C
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• pp.889-896
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• 2006

The crest factor distribution of orthogonal frequency division multiplexing (OFDM) symbol sequences is evaluated and it is shown that OFDM symbol sequences with a short period are expected to have a high crest factor. The crest factor relationship between two input symbol sequences, Hamming distance D apart is also derived. Using these two results, we propose two criteria for a phase sequence set of the selected mapping (SLM) scheme and suggest the rows of the cyclic Hadamard matrix constructed from an m-sequence as the near optimal phase sequence set of the SLM scheme.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.601-603
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• 1998

In this paper, Hadamard transform imaging spectrometers utilizing Grill spectrometers are proposed. General Hadamard Transform Spectrometers (HTS) carry out one-encoding through input masks, but Grill spectrometers carry out double-encoding through entrance and exit masks. Thus Grill spectrometers increase the signal-to-noise ratio by double-encoding. we reconfigure the system by using the Grill spectrometers which use a left cyclic S-matrix instead of the conventional right cyclic one. Then, we model the system and apply the mask characteristics method, i.e. $T^{I}$ method, to complete fast algorithm. Through computer simulations, we want to prove the superiority of the proposed system by comparing with the conventional HTS. From Observations concerning the average mean square error(AMSE) associated with estimates from the $T^{I}$ spectrum-recovery method, the relative performances of the two systems are compared.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.2A
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• pp.116-123
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• 2002

The jacket matrix is based on the Walsh-Hadamard matrix and an extension of it. While elements of the Walsh-Hadamard matrix are +1, or -1, those of the Jacket matrix are ${\pm}$1 and ${\pm}$$\omega$, which is $\omega$, which is ${\pm}$j and ${\pm}$2$\sub$n/. This matrix has weights in the center part of the matrix and its size is 1/4 of Hadamard matrix, and it has also two parts, sigh and weight. In this paper, instead of the conventional Jacket matrix where the weight is imposed by force, a simple Jacket sequence generation method is proposed. The Jacket sequence is generated by AND and Exclusive-OR operations between the binary indices bits of row and those of column. The weight is imposed on the element by when the product of each Exclusive-OR operations of significant upper two binary index bits of a row and column is 1. Each part of the Jacket matrix can be represented by jacket sequence using row and column binary index bits. Using Distributed Arithmetic (DA), we present a VLSI architecture of the Fast Jacket transform is presented. The Jacket matrix is able to be applied to cryptography, the information theory and complex spreading jacket QPSK modulation for WCDMA.