• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.397-404
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• 2016

In this work, a method is given to construct quantum codes from cyclic codes over F₄ + vF₄ which will be denoted as R throughout the paper, where v² = v and a Gray map is defined between R and where F₄ is the field with 4 elements. Some optimal quantum code parameters and others will be presented at the end of the paper.

• 한국통신학회논문지
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• 제41권12호
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• pp.1745-1747
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• 2016

본 논문에서 다양한 블록 크기를 가지는 완전 차집합군을 이용하여 불규칙 준순환 패리티 체크 부호를 생성하는 방법을 제안한다. 제안하는 부호는 기존의 설계방법들에 비해 부호율, 부호 길이, 차수 분포 측면에서 다양한 값들을 가질 수 있다는 장점을 보인다. 또한 랜덤한 방법으로 설계하기 힘든 매우 짧은 길이의 부호를 체계적으로 설계할 수 있다. 모의실험을 통해 제안하는 부호의 오류 정정 성능을 검증한다.

• 대한수학회보
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• 제56권2호
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• pp.285-301
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• 2019

Let $p_1$ and $p_2$ be two distinct odd primes with gcd($p_1-1$, $p_2-1$) = 6. In this paper, we compute the linear complexity of the first class two-prime Whiteman's generalized cyclotomic sequence (WGCS-I) of order d = 6. Our results show that their linear complexity is quite good. So, the sequence can be used in many domains such as cryptography and coding theory. This article enrich a method to construct several classes of cyclic codes over GF(q) with length $n=p_1p_2$ using the two-prime WGCS-I of order 6. We also obtain the lower bounds on the minimum distance of these cyclic codes.

• 한국통신학회논문지
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• 제36권10C호
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• pp.605-613
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• 2011

잡음에 있는 채널을 통한 디지털 통신에서는 채널 잡음에 대항하기 위해 오류정정부호(채널부호)를 사용하게 된다. 만일 송신측의 협조 없이 전송정보를 알아내려면 사용된 채널부호를 복원하는 것이 무엇보다 중요하다. 본 논문에서는 잡음에 오염된 수신 비트열로부터 사용된 채널부호의 여려 파라메타를 추출하여 궁극적으로 채널부호를 복원하는 채널부호 복원기법 중 순회부호(cyclic code)의 복원 기법을 제안한다.

• Journal of Communications and Networks
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• 제12권5호
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• pp.406-410
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• 2010

This paper presents an approach to the construction of non-binary quasi-cyclic (QC) low-density parity-check (LDPC) codes based on multiplicative groups over one Galois field GF(q) and Euclidean geometries over another Galois field GF($2^S$). Codes of this class are shown to be regular with girth $6{\leq}g{\leq}18$ and have low densities. Finally, simulation results show that the proposed codes perform very wel with the iterative decoding.

• 대한전자공학회논문지TC
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• 제47권11호
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• pp.36-42
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• 2010

이 논문은 유클리드 기하학과 Circulant Permutation Matrices에서 병렬 구성을 기반으로 하는 Quasi-cyclic Low-density parity-check (QC-LDPC) 코드의 생성을 위한 하이브리드한 접근방식을 나타낸다. 이 방법으로 생성된 코드는 넓은 둘레(Large Girth)와 저밀도(Low Density)를 가진 규칙적인 코드로 나타내어진다. 시뮬레이션 결과는 이 코드들이 반복 복호(Iterative Decoding)를 통해 좋은 성능을 갖는것과 부호화되지 않은 시스템에서 좋은 코딩 이득을 달성하는 것을 보인다.

• 제어로봇시스템학회논문지
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• 제8권4호
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• pp.299-302
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• 2002

Error detection and correction using CRC and the general class of cyclic codes is an important part of designing reliable data transmission schemes. The decoding method for cyclic codes using covering patterns is easily-implementable, and its complexity de-pends on the number of covering patterns employed. Determination of the minimal set of covering patterns for a given code is an open problem. In this paper, an efficient search method for constructing minimal sets of covering patterns is proposed and compared with several existing search methods. The result is applicable to various codes of practical interest.

• 대한수학회지
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• 제46권1호
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• pp.13-30
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• 2009

A subset of n tuples of elements of ${\mathbb{Z}}_9$ is said to be a code over ${\mathbb{Z}}_9$ if it is a ${\mathbb{Z}}_9$-module. In this paper we consider an special family of cyclic codes over ${\mathbb{Z}}_9$, namely quadratic residue codes. We define these 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 finite fields.

• 대한수학회보
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• 제50권5호
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• pp.1513-1521
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• 2013

In this paper we will study cyclic codes over some special rings: $\mathbb{F}_q[u]/(u^i)$, $\mathbb{F}_q[u_1,{\ldots},u_i]/(u^2_1,u^2_2,{\ldots},u^2_i,u_1u_2-u_2u_1,{\ldots},u_ku_j-u_ju_k,{\ldots})$, and $\mathbb{F}_q[u,v]/(u^i,v^j,uv-vu)$, where $\mathbb{F}_q$ is a field with $q$ elements $q=p^r$ for some prime number $p$ and $r{\in}\mathbb{N}-\{0\}$.

• Journal of Communications and Networks
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• 제13권3호
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• pp.205-210
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• 2011

This paper presents an approach to the construction of multiple-rate quasi-cyclic low-density parity-check (LDPC) codes. Parity-check matrices of the proposed codes consist of $q{\times}q$ square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (${\mu}$-fiats) and points in Euclidean geometries, respectively. By decomposing the ${\mu}$-fiats, we obtain LDPC codes of different code rates and a constant code length. The code performance is investigated in term of the bit error rate and compared with those of LDPC codes given in IEEE standards. Simulation results show that our codes perform very well and have low error floors over the additive white Gaussian noise channel.