• Korean Journal of Mathematics
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• 제11권1호
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• pp.57-64
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• 2003

We define $Z_16$ quadratic residue codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over a field.

• Journal of information and communication convergence engineering
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• 제4권4호
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• pp.136-140
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• 2006

In this paper, we consider the detection of orthogonal space-time block codes (OSTBCs) without channel state information (CSI) at the receiver. Based on the conventional blind cyclic decoder, we propose an enhanced blind cyclic decoder which has higher system performance than the conventional one. Furthermore, the proposed decoder offers low complexity since it does not require the computation of singular value decomposition.

• 대한수학회논문집
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• 제28권1호
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• pp.39-54
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• 2013

The purpose of this paper is to find a description of the cyclic codes of length $2^n$ over $\mathbb{Z}_4$. We show that any ideal of $\mathbb{Z}_4$[X]/($X^{2n}$ - 1) is generated by at most two polynomials of the standard forms. We also find an explicit description of their duals in terms of the generators.

• 대한수학회지
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• 제44권3호
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• pp.697-706
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• 2007

In [8], we showed that any ideal of $\mathbb{Z}_4[X]/(X^{2^n}-1)$ is generated by at most two polynomials of the standard forms. The purpose of this paper is to find a description of the cyclic codes of even length over $\mathbb{Z}_4$ namely the ideals of $\mathbb{Z}_4[X]/(X^l\;-\;1)$, where $l$ is an even integer.

• ETRI Journal
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• 제29권3호
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• pp.381-389
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• 2007

In this paper we propose a graph-theoretic method based on linear congruence for constructing low-density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ${\rho}$)-regular quasi-cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit-error-rate performance with iterative decoding in additive white Gaussian noise channels.

• Journal of Communications and Networks
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• 제16권3호
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• pp.249-257
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• 2014

This paper presents methods to the construction of regular and irregular low-density parity-check (LDPC) codes based on Euclidean geometries over the Galois field. Codes constructed by these methods have quasi-cyclic (QC) structure and large girth. By decomposing hyperplanes in Euclidean geometry, the proposed irregular LDPC codes have flexible column/row weights. Therefore, the degree distributions of proposed irregular LDPC codes can be optimized by technologies like the curve fitting in the extrinsic information transfer (EXIT) charts. Simulation results show that the proposed codes perform very well with an iterative decoding over the AWGN channel.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.99-110
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• 1998

In this paper we study cyclic codes in $Z_m$. i.e., ideals in $Z_mG$, G afinite abelian group and we give a classification of such codes. We also sgtudy the minimum Hamming distance and the generalized Hamming weight of BCH codes over $Z_m$.

• ETRI Journal
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• 제45권3호
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• pp.404-417
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• 2023

This paper proposed a novel method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes of medium to high code rates that can be applied in cloud data storage systems, requiring better error correction capabilities. The novelty of this method lies in the construction of sparse base matrices, using a girth greater than 4 that can then be expanded with a lift factor to produce high code rate QC-LDPC codes. Investigations revealed that the proposed large-sized QC-LDPC codes with high code rates displayed low encoding complexities and provided a low bit error rate (BER) of 10^-10 at 3.5 dB E_b/N₀ than conventional LDPC codes, which showed a BER of 10^-7 at 3 dB E_b/N₀. Subsequently, implementation of the proposed QC-LDPC code in a softwaredefined radio, using the NI USRP 2920 hardware platform, was conducted. As a result, a BER of 10^-6 at 4.2 dB E_b/N₀ was achieved. Then, the performance of the proposed codes based on their encoding-decoding speeds and storage overhead was investigated when applied to a cloud data storage (GCP). Our results revealed that the proposed codes required much less time for encoding and decoding (of data files having a 10 MB size) and produced less storage overhead than the conventional LDPC and Reed-Solomon codes.

• 대한수학회지
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• 제51권4호
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• pp.853-866
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• 2014

Constacyclic codes of length $p^s$ over $R=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m}$ are precisely the ideals of the ring $\frac{R[x]}{<x^{p^s}-1>}$. In this paper, we investigate constacyclic codes of length $p^s$ over R. The units of the ring R are of the forms ${\gamma}$, ${\alpha}+u{\beta}$, ${\alpha}+u{\beta}+u^2{\gamma}$ and ${\alpha}+u^2{\gamma}$, where ${\alpha}$, ${\beta}$ and ${\gamma}$ are nonzero elements of $\mathbb{F}_{p^m}$. We obtain the structures and Hamming distances of all (${\alpha}+u{\beta}$)-constacyclic codes and (${\alpha}+u{\beta}+u^2{\gamma}$)-constacyclic codes of length $p^s$ over R. Furthermore, we classify all cyclic codes of length $p^s$ over R, and by using the ring isomorphism we characterize ${\gamma}$-constacyclic codes of length $p^s$ over R.

• 한국통신학회논문지
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• 제35권2B호
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• pp.325-333
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• 2010

Wibro를 포함한 많은 시스템에서 순환 치환 행렬(circulant)로 구성된 준 순환 LDPC(low-density parity-check) 부호를 사용하고 있다. 하지만 준 순환 부호의 기저 행렬 크기의 제약으로 인해 계층 복호(layered decoding)가 가능하고 일정 값 이상의 거스(girth)를 만족하면서 동시에 최적의 차수 분포를 갖도록 하는 것은 매우 힘들다. 본 논문에서는 이러한 문제점을 극복하기 위해 중첩 행렬(superposition matrix) 구조를 가지는 준 순환 LDPC 부호를 제안한다. 중첩 행렬을 이용할 경우에 특화된 거스 점검 조건들을 유도하고, 기존 행렬 구조와 중첩 행렬 구조 두 가지 모두에 대해 계층 복호를 수행할 수 있는 새로운 LDPC 복호기 구조를 제안한다. 모의실험을 통하여 중첩 행렬 구조를 가지는 LDPC 부호는 복호 시 수렴 속도가 개선되고 오류 정정율이 향상됨을 보인다.