• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.29-44
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• 2021

The set D of column vectors of a generator matrix of a linear code is called a defining set of the linear code. In this paper we consider the problem of constructing few-weight (mainly two- or three-weight) linear codes from defining sets. It can be easily seen that we obtain an one-weight code when we take a defining set to be the nonzero codewords of a linear code. Therefore we have to choose a defining set from a non-linear code to obtain two- or three-weight codes, and we face the problem that the constructed code contains many weights. To overcome this difficulty, we employ the linear codes of the following form: Let D be a subset of ��2n, and W (resp. V ) be a subspace of ��2 (resp. ��2n). We define the linear code ��D(W; V ) with defining set D and restricted to W, V by $${\mathcal{C}}_D(W;V )=\{(s+u{\cdot}x)_{x{\in}D^{\ast}}|s{\in}W,u{\in}V\}$$. We obtain two- or three-weight codes by taking D to be a Vasil'ev code of length n = 2m - 1(m ≥ 3) and a suitable choices of W. We do the same job for D being the complement of a Vasil'ev code. The constructed few-weight codes share some nice properties. Some of them are optimal in the sense that they attain either the Griesmer bound or the Grey-Rankin bound. Most of them are minimal codes which, in turn, have an application in secret sharing schemes. Finally we obtain an infinite family of minimal codes for which the sufficient condition of Ashikhmin and Barg does not hold.

• East Asian mathematical journal
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• v.17 no.1
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• pp.167-174
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• 2001

We find the generalized Hamming weights of cyclic linear q-ary codes which are generated by a codeword of weight 2, and of any length.

• ETRI Journal
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• v.32 no.4
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• pp.588-595
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• 2010

This paper proposes encoding and decoding for nonlinear product codes and investigates the performance of nonlinear product codes. The proposed nonlinear product codes are constructed as N-dimensional product codes where the constituent codes are nonlinear binary codes derived from the linear codes over higher order alphabets, for example, Preparata or Kerdock codes. The performance and the complexity of the proposed construction are evaluated using the well-known nonlinear Nordstrom-Robinson code, which is presented in the generalized array code format with a low complexity trellis. The proposed construction shows the additional coding gain, reduced error floor, and lower implementation complexity. The (64, 24, 12) nonlinear binary product code has an effective gain of about 2.5 dB and 1 dB gain at a BER of $10^{-6}$ when compared to the (64, 15, 16) linear product code and the (64, 24, 10) linear product code, respectively. The (256, 64, 36) nonlinear binary product code composed of two Nordstrom-Robinson codes has an effective gain of about 0.7 dB at a BER of $10^{-5}$ when compared to the (256, 64, 25) linear product code composed of two (16, 8, 5) quasi-cyclic codes.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.2
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• pp.152-161
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• 2009

As follow jamming signals in a FHSS system cause malfuctioning in the code tracking circuits using early-late gates, we need a code tracking circuit that is robust against the follow jamming signals. In this paper, we propose a code tracking circuit using a linear clipper-Gaussian filter algorithm to remedy the malfunctioning due to the follow jamming signals in FHSS systems. We investigate the mechanism of the malfunctioning of the code tracking circuit and verify that the proposed linear clipper-Gaussian filter metigates the problem through mathematical analysis and computer simulations.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.107-120
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• 2008

There has been a recent growth of interest in codes with respect to a newly defined non-Hamming metric grown as the Rosenbloom-Tsfasman metric (RT, or $\rho$, in short). In this paper, the definitions of the Lee complete $\rho$ weight enumerator and the exact complete $\rho$ weight enumerator of a code over $M_n_\times_s(Z_4)$ are given, and the MacWilliams identities with respect to this RT metric for the two weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are proven too. At last, we also prove that the MacWilliams identities for the Lee and exact complete $\rho$ weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are the generalizations of the MacWilliams identities for the Lee and complete weight enumerators of the corresponding code over $Z_4$.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.1 no.1
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• pp.77-83
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• 1997

In this paper, we present a comparison between QCELP(Qualcomm Code Excited Linear Predictor) speech coder that is operating in digital mobile communication system and CS-ACELP(Conjugate Structure Algebraic Code Excited Linear Prediction) speech coder that is scheduled to use for IMT-2000 (International Mobile Telecommunications 2000) system. The performance comparison might give help to design of the speech coding algorithms so that the robustness of the algorithms to channel errors engaged by mobile communication system be optimized.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.9
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• pp.1348-1357
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• 1993

In this paper, we present code-excited linear prediction coding using trellis coded vector excitation, termed trellis code-excited linear prediction coding (TCELP), for an efficient 8 kbps digital cellular vocoder. A training sequence-based algorithm is developed for designing an optimized codebook subject to the TCELP structure. Also, we discuss the encoding complexity of the TCELP system and trellis symbol release rules that avoid excessive encoding delay. finally, simulation results results for the TCELP coder are given at the bit rate of 8 kbps.

• Journal of Communications and Networks
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• v.1 no.3
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• pp.153-157
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• 1999

In this paper, we derive finite-dimensional non-linear fil-ters for optimally reconstructing speech signals in Switched Predic-tion vocoders, Code Excited Linear Prediction(CELP) and Differ-ential Pulse Code Modulation (DPCM). Our filter is an extension of the Hidden Markov filter.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.493-505
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• 2000

We discuss the class of projective systems whose supports are the complement of the union of two linear subspaces in general position. We express the weight enumerators of the codes generated by these projective systems using two simplex codes corresponding to given linear subspaces. We also prove these codes are uniquely determined upto equivalence by their weight enumerators.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.1
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• pp.96-102
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• 1995

This paper presents the VHSIC Hardware Description Language(VHDL) implementation of the Fixed Point Covariance Lattice(FLAT) algorithm for an Linear Predictive Coding(LPC) analysis and its related algorithms, such as the forth order high pass Infinite Impulse Response(IIR) filter, covariance matrix calculation, and Spectral Smoothing Technique(SST) in the Vector Sum Exited Linear Predictive(VSELP) speech coder that has been Selected as the standard speech coder for the North America and Japanese digital cellular. Existing Digital Signal Processor(DSP) chips used in digital cellular phones are derived from general purpose DSP chips, and thus, these DSP chips may not be optimal and effective architectures are to be designed for the above mentioned algorithms. Then we implemented the VHDL code based on the C code, Finally, we verified that VHDL results are the same as C code results for real speech data. The implemented VHDL code can be used for performing logic synthesis and for designing an LPC Application Specific Integrated Circuit(ASOC) chip and DsP chips. We first developed the C language code to investigate the correctness of algorithms and to compare C code results with VHDL code results block by block.