• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.2
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• pp.271-277
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• 2012

In this paper, we introduce the extended sequences of sequences generated by GMW sequences and No sequences. And we analyze cross-correlatons of the extended sequences. Also we give extended sequences which are constructed from Legendre sequences. This is helpful to a cryptosystem and a communication system. Particularly this study is useful to the CDMA system signal design.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.10
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• pp.2181-2187
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• 2011

In this paper, a family of binary sequences generated by GMW sequences and No sequences is introduced and analyzed. Each sequence within a family has period $N=2^n-1$, n=2m and there are $2^m$ sequences within that family. We obtain auto and cross-correlation values and linear span of the synthesized sequence.

• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.4
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• pp.539-544
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• 2011

Balanced binary sequences of period $2^n-1(n{\geq}1)$ having the two-valued autocorrelation function have many applications in spread-spectrum communications system. In this paper we propose new nonlinear binary sequences which are constructed from Legendre sequences with the same cross-correlation as the sequences proposed by Cho. These sequences include the m-sequences, GMW sequences, Kasami sequences and No sequences which are described in terms of the trace function over a finite field. Also the proposed sequences have more low cross-correlation distribution than the quadratic form sequences proposed by Klapper.

• Journal of Electrical Engineering and information Science
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• v.2 no.6
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• pp.217-222
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• 1997

Recently, No et al. presented a new construction of binary sequences with ideal autocorrelation property. In this paper, we applied this method into some of the well-known binary sequences with ideal autocorrelation, and the results are described in detail. First, the GMW sequences are shown to be a natural extension of m-sequences with respect to this method. Second, new binary sequences with ideal autocorrelation property are explicitly constructed from Legendre sequences, Hall's sextic residue sequences, and other known sequences of miscellaneous type.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.845-848
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• 2023

Erratum/Addendum to the paper "Biisometric operators and biorthogonal sequences" [Bull. Korean Math. Soc. 56 (2019), No. 3, pp. 585-596].

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.6
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• pp.1273-1278
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• 1997

Pseudonoise sequences of period 2$^{m}$ -1 with idel autocorrelation have been researched such as m-sequences, GMW sequences, Legendre sequences, and extended sequences. The m-sequences, the GMW sequences, the Legendre sequences, and the extended sequences are best described in terms of the trace function by previous works. Besides, there are Hall's sextic residue sequences and miscellaneous sequences with ideal autocorrelation, whose general constructions are not known so far. However, are are no explicit descripton of the Hall's sextic residue sequences and the miscellaneous sequences in terms of the trace function. In this paper, the Hall's sextic residue sequences and the miscellaneous sequences of period 2$^{m}$ -1 are expressed as a sum of trace functions. The miscellaneous sequences with ideal autocorrelation, which are newly found by computer search, are also expressed as a sum of trace functions.

• The KIPS Transactions:PartD
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• v.14D no.7
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• pp.727-732
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• 2007

Most of previous work on indexing and searching time series focused on the similarity matching and retrieval of one-attribute time series. However, multimedia databases such as music, video need to handle the similarity search in multi-attribute time series. The limitation of the current similarity models for multi-attribute sequences is that there is no consideration for attributes' sequences. The multi-attribute sequences are composed of several attributes' sequences. Since the users may want to find the similar patterns considering attributes's sequences, it is more appropriate to consider the similarity between two multi-attribute sequences in the viewpoint of attributes' sequences. In this paper, we propose the similarity search method based on attributes's sequences in multi-attribute time series databases. The proposed method can efficiently reduce the search space and guarantees no false dismissals. In addition, we give preliminary experimental results to show the effectiveness of the proposed method.

• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.1
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• pp.13-19
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• 2011

Games gave the calculation method for the crosscorrelation function of a Kasami sequence and a No sequence that have been generated by the same primitive polynomial. In this paper, we calculate the crosscorrelation function of a Kasami sequence and a No sequence that have been generated by the same primitive polynomial with the periodic crosscorrelation function of two base sequences. Our method is different from the Games's method.

• Investigative Magnetic Resonance Imaging
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• v.24 no.3
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• pp.141-153
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• 2020

Purpose: Myocardial T1 and T2 relaxation times are affected by technical factors such as cardiovascular magnetic resonance platform/vendor. We aimed to validate T1 and T2 mapping sequences using a phantom; establish reference T1, T2, and extracellular volume (ECV) measurements using two sequences at 3T in normal Koreans; and compare the protocols and evaluate the differences from previously reported measurements. Materials and Methods: Eleven healthy subjects underwent cardiac magnetic resonance imaging (MRI) using 3T MRI equipment (Verio, Siemens, Erlangen, Germany). We did phantom validation before volunteer scanning: T1 mapping with modified look locker inversion recovery (MOLLI) with 5(3)3 and 4(1)3(1)2 sequences, and T2 mapping with gradient echo (GRE) and TrueFISP sequences. We did T1 and T2 mappings on the volunteers with the same sequences. ECV was also calculated with both sequences after gadolinium enhancement. Results: The phantom study showed no significant differences from the gold standard T1 and T2 values in either sequence. Pre-contrast T1 relaxation times of the 4(1)3(1)2 protocol was 1142.27 ± 36.64 ms and of the 5(3)3 was 1266.03 ± 32.86 ms on the volunteer study. T2 relaxation times of GRE were 40.09 ± 2.45 ms and T2 relaxation times of TrueFISP were 38.20 ± 1.64 ms in each. ECV calculation was 24.42% ± 2.41% and 26.11% ± 2.39% in the 4(1)3(1)2 and 5(3)3 protocols, respectively, and showed no differences at any segment or slice between the sequences. We also calculated ECV from the pre-enhancement T1 relaxation time of MOLLI 5(3)3 and the post-enhancement T1 relaxation time of MOLLI 4(1)3(1)2, with no significant differences between the combinations. Conclusion: Using phantom-validated sequences, we reported the normal myocardial T1, T2, and ECV reference values of healthy Koreans at 3T. There were no statistically significant differences between the sequences, although it has limited statistical value due to the small number of subjects studied. ECV showed no significant differences between calculations based on various pre- and post-mapping combinations.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.7C
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• pp.534-539
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• 2008

For an odd prime p, n=4k, and $d=((p^{2k}+1)/2)^2$, Seo, Kim, No, and Shin derived the correlation distribution of p-ary m-sequence of period $p^n-1$ and its decimated sequences by d. In this paper, two new families of p-ary sequences with family size $p^{2k}$ and maximum correlation magnitude $[2]sqrt{p^n}-1$ are constructed. The linear complexity of new p-ary sequences in the families are derived in the some cases and the upper and lower bounds of their linear complexity for general cases are presented.