• 충청수학회지
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• 제25권4호
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• pp.633-642
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• 2012

We give the complete classification of binary formally self-dual even codes of length 18. There are exactly 26568 inequivalent such codes. This completes the classification of binary formally self-dual even codes of length up to 18.

• 대한수학회보
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• 제54권1호
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• pp.29-42
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• 2017

In this work, four circulant and quadratic double circulant (QDC) constructions are applied to the family of the rings $R_{k,m}$. Self-dual binary codes are obtained as the Gray images of self-dual QDC codes over $R_{k,m}$. Extremal binary self-dual codes of length 64 are obtained as Gray images of ${\lambda}-four$ circulant codes over $R_{2,1}$ and $R_{2,2}$. Extremal binary self-dual codes of lengths 66 and 68 are constructed by applying extension theorems to the ${\mathbb{F}}_2$ and $R_{2,1}$ images of these codes. More precisely, 10 new codes of length 66 and 39 new codes of length 68 are discovered. The codes with these weight enumerators are constructed for the first time in literature. The results are tabulated.

• 한국통신학회논문지
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• 제21권10호
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• pp.2653-2659
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• 1996

In this paper, DC-free and minimum bandwidth binary line codes with look-up table are proposed and their performances are analyzed. As results of performance analysis, the proposed codes are shown to have spectral nulls at DC and Nyquist frequency. Among the proposed codes, binary line codes of which both codeword digital sum and alternating digital sum are zero have lower code rate but better spectral characteristics. Furthermore, binary line codes which consist of all codewords including those with nonzero digital sum and alternating digital sum have worese spectral characteristics but higher code rate.

• 대한수학회보
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• 제51권4호
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• pp.1175-1186
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• 2014

We construct new binary optimal self-dual codes of length 50. We develop a construction method for binary self-dual codes with a fixed-point-free automorphism of order 2. Using this method, we find new binary optimal self-dual codes of length 52. From these codes, we obtain Lee-optimal self-dual codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$ of lengths 25 and 26.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.85-95
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• 2019

In this paper, we define near-minimal shadow and study the existence problem of extremal Type I binary self-dual codes with near-minimal shadow. We prove that there is no such codes of length n = 24m + 2($m{\geq}0$), n = 24m + 4($m{\geq}9$), n = 24m + 6($m{\geq}21$), and n = 24m + 10($m{\geq}87$).

• 한국통신학회논문지
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• 제31권4C호
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• pp.426-433
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• 2006

본 논문에서는 이중이진 터보부호를 오류정정부호로 사용하는 이중이진 터보 incremental redundancy(IR)-hybrid ARQ(HARQ)기법을 제안한다. 또한 HARQ의 성능파라미터인 처리율의 기본적 해석 방법을 제시한다. 제안된 이중이진 터보 IR-HARQ는 이진 터보부호를 사용하는 IR-HARQ에 비해 모든 $E_s/N_0$ 영역에서 향상된 처리율을 보이며 오류정정부호만을 사용하는 경우에 비해 부호화 이득을 향상시킨다.

• 대한수학회지
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• 제39권2호
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• pp.289-317
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• 2002

We associate binary codes to polynomials over fields of characteristic two and show that the binary Golay codes are associated to the Mathieu group polynomials in characteristics two. We give two more polynomials whose Galois group in $M_{12}$ but different self-orthogonal binary codes are associated. Also, we find a family of $M_{24}$-coverings which includes previous ones.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 ITC-CSCC -3
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• pp.1705-1708
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• 2002

Spreading codes with ZCD(zero-correlation duration) property have the MAI(multiple access interference) rejection ability in the CDMA systems. A class of multi-level spreading codes, i.e., Zero padded ternary ZCD codes are introduced in this paper. By the selected zero-padding method to the binary ZCD codes, ternary ZCD codes are generated and they have enhanced ZCD property and family size than the binary ZCD codes.

• 대한수학회보
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• 제60권3호
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• pp.829-844
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• 2023

In this paper, we present a new construction for self-dual codes that uses the concept of double bordered construction, group rings, and reverse circulant matrices. Using groups of orders 2, 3, 4, and 5, and by applying the construction over the binary field and the ring F₂ + uF₂, we obtain extremal binary self-dual codes of various lengths: 12, 16, 20, 24, 32, 40, and 48. In particular, we show the significance of this new construction by constructing the unique Extended Binary Golay Code [24, 12, 8] and the unique Extended Quadratic Residue [48, 24, 12] Type II linear block code. Moreover, we strengthen the existing relationship between units and non-units with the self-dual codes presented in [10] by limiting the conditions given in the corollary. Additionally, we establish a relationship between idempotent and self-dual codes, which is done for the first time in the literature.

• ETRI Journal
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• 제32권4호
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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.