• Korean Journal of Mathematics
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• v.22 no.4
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• pp.725-742
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• 2014

In this paper, we find all inequivalent classes of self-orthogonal codes over $Z_{p^2}$ of lengths $l{\leq}3$ for all primes p, using similar method as in [3]. We find that the classification of self-orthogonal codes over $Z_{p^2}$ includes the classification of all codes over $Z_p$. Consequently, we classify all the codes over $Z_p$ and self-orthogonal codes over $Z_{p^2}$ of lengths $l{\leq}3$ according to the automorphism group of each code.

• Proceedings of the KIEE Conference
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• 2001.11c
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• pp.187-190
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• 2001

A new ultrasound imaging technique based on simultaneous multiple transmit focusing using orthogonal modified Golay codes is presented. modified Golay codes are used to increase signal-to-noise-ratio(SNR) and maximize the transmit power efficiency(TPE). Conventional Golay codes consist of a pair of complementary codes with same length and can be compressed into a delta-like signal due to their complementary property. In the present work, two modified Golay codes focused at different depths are transmitted at the same time, which are mutually orthogonal. On receive, these orthogonal modified Golay codes are separately compressed into two short pulses and individually focused. These two focused beam are combined to form a frame of image with improved lateral resolution. Computer simulations are performed to verity the proposed method improves the lateral resolution of image compared with the conventional echo system.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.201-209
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• 2017

There exists already mass formula which is the number of self orthogonal codes in $GF(q)^n$, but not proof of it. In this paper we described some theories about finite geometry and by using them proved the mass formula when $q=p^m$, p is odd prime.

• Communications of Mathematical Education
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• v.6
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• pp.371-381
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• 1997

Let p be an odd prime number. We introduce simple and useful decoding algorithm for orthogonal Latin square codes of order p. Let H be the parity check matrix of orthogonal Latin square code. For any x ${\in}$ GF(p)$^{n}$, we call xH$^{T}$ the syndrome of x. This method is based on the syndrome decoding for linear codes. In L$_{p}$, we need to find the first and the second coordinates of codeword in order to correct the errored received vector.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.193-204
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• 2022

We present construction methods for free self-orthogonal (self-dual or Type II) codes over ℤ₄[v]/〈v² + 2v〉 which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on ℤ₄, we give a construct method for a code over ℤ₄. We have some new and optimal codes over ℤ₄ with respect to the minimum Lee weight or minimum Euclidean weight.

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.4
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• pp.304-312
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• 2008

Orthogonal codes like Walsh and Golay codes may have large correlation value when they are not synchronized, hence they are seldom used in asynchronous CDMA systems. Wysocki[1] showed that by multiplying the original Walsh-Hadamard matrix with an orthogonal transformation matrix the resultant matrix sustains orthogonality between row vectors and their cross-correlation can be reduced. Soberly and Wysocki[2] proposed similar scheme on Golay codes. This implies that using the proper orthogonal transformation cross-correlation of Walsh and Golay codes can be reduced, and the transformed codes can be used for user separation in the CDAM reverse link. In this paper we discuss cross-correlation related parameters which affect the performance of an asynchronous CDMA link, and we investigate the correlation properties of the transformed codes. When we designed orthogonal transformation matrices for Walsh and Golay codes, we minimized the maximum value of aperiodic cross-correlation of the codes ($ACC_{max}$) or the mean square value of the aperiodic cross-correlation($R_{cc}$) with preserving the orthogonality of the modified codes. We also evaluate the asynchronous CDMA system that uses the transformed Walsh and Golay codes.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.9 no.1
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• pp.34-41
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• 2010

In this paper, we analyze and simulate co-channel interference (CCI) mitigation method for cooperative communication systems employing decode-and-forward relays. In co-channel interference mitigation method, A source transmits signals that are encoded by orthogonal code. Then, the receiver can distinguish its own signals form the received signals by using the orthogonal code which is already known to the receiver. The orthogonal codes applied to this paper are orthogonal Gold codes. However, we can employ other codes, which have orthogonality, as the orthogonal code. In addition, we utilize a space time block coding (STBC) scheme for enhancing the system performance by obtaining additional array gain.

• Journal of Communications and Networks
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• v.10 no.3
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• pp.253-257
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• 2008

In this paper, the performance of generic orthogonal space-time block codes (OSTBCs) introduced by Alamouti [2], Tarokh [3], and Su and Xia [11] is analyzed. We first define one-dimensional component symbol error function (ODSEF) from the exact expression of the pairwise error probability of an OSTBC. Utilizing the ODSEF and the bit error probability (BEP) expression for quadrature amplitude modulation (QAM) introduced by Cho and Yoon [9], the exact closed-form expressions for the BEP of linear OSTBCs with QAM in quasi-static Rayleigh fading channel are derived. We also derive the exact closed-form of the BEP for some OSTBCs which have at least one message symbol transmitted with unequal power via all transmit antennas.

• Journal of the Korean Statistical Society
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• v.32 no.3
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• pp.225-233
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• 2003

In this paper we make use of the parity check matrices of the codes based on inverting construction $Y_1$ to construct a number of new asymmetric orthogonal arrays with higher strength and higher number of levels using the method of construction of asymmetric orthogonal arrays given by Suen et al. (2001).

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.3
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• pp.40-45
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• 2008

This paper proposes the signal design techniques of quasi-orthogonal space time block codes (QO-STBCS) on the multi-dimensional signal space. In the multiple antenna system(MIMO), QO-STBC achieves the full-diversity and full-rate by grouping two based-symbols. We study the condition for the full-diversity of the grouping QO-STBC geometrically and the performance analysis of codes on the multi-dimensional signal space regarding the various signal constellations. Simulation results show that the way of the performance analysis is validity.