• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.91-98
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• 2010

One of the most interesting classes of algebraic codes is the class of quadratic residue (QR) codes over a finite field. A natural construction doubling the lengths of QR codes seems to be the double circulant constructions based on quadratic residues given by Karlin, Pless, Gaborit, et. al. In this paper we define a class of triple circulant linear codes based on quadratic residues. We construct many new optimal codes or codes with the highest known parameters using this construction. In particular, we find the first example of a ternary [58, 20, 20] code, which improves the previously known highest minimum distance of any ternary [58, 20] codes.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.273-275
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• 2008

We will give a short and elementary proof of the existence of infinitely many primes p such that a given positive integer a congruent 3 modulo 4 is a quadratic non-residue modulo p.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.155-164
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• 2003

A method is proposed to predict the distances between given residue pairs (between C$\sub$${\alpha}$/ atoms) of a protein using a sequence to structure mapping by indefinite quadratic approximation. The prediction technique requires a data fitting in three dimensional space with coordinates of the residues of known structured proteins and leads to a numerical ref resentation of 20 amino acids by minimizing a large least norm iteratively. These approximations are used in distance prediction for given residue pairs. Some computational experience on a test set of small proteins from Brookhaven Protein Data Bank are given.

• The KIPS Transactions:PartC
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• v.19C no.4
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• pp.225-230
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• 2012

Since one of weak points of public crypto-systems is to require the verification of public key, identity based crypto-systems were proposed as an alternative. However, such techniques need a private key generator which can be a single point of failure. To improve such weakness, threshold identity-based crypto-systems were proposed. In this paper, we propose a new threshold identity-based encryption scheme which is constructed to extend an identity-based encryption scheme by Cocks. Since the proposed scheme is based on quadratic residues, it has smaller complexity of encryption. And we prove that the proposed scheme is secure against a chosen identity attack.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.437-449
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• 2009

In this paper, we calculate the number of points on elliptic curves $E^{a^3}_0:y^2=x^3+a^3$ over ${\mathbb{F}}_p$ mod 24 and $E^b_0:y^2=x^3+b$ over ${\mathbb{F}}_p$ mod 6, where b is cubic non-residue in ${\mathbb{F}}^*_p$. For example, if p ${\equiv}$ 1 (mod 12) is a prime, and a and a(2t - 3) are quadratic residues modulo p with $3t^2{\equiv}1$ (mod p), then the number of points in $E^{a^3}_0:y^2=x^3+a^3$ is congruent to 0 modulo 24.

• Asian Journal of Turfgrass Science
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• v.6 no.1
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• pp.29-37
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• 1992

This experiment was carried out in order to study the changes of morphological characters of the growth and thatch accumulation in :3 varieties of Kentucky bluegrass under removing clipping residues as affected by cutting management. The varieties used were Park, Kenhiuc and Newport.The results obtained are as follows; 1. The dry weight of leaf. stem and number of tiller was highest at 22. June and lowest at 21. Aug in alt varieties. And then the dry weight of rhizome, root and thatch increased with growth progressed) Tabte 3). 2. The relationship of the dry weight of biological yield and number of tillers was quadratic ally increased in the growth stage of spring($R^2$= 0.982**), and linearlly increased in the growth stage of autumn(r 0.944*)(Fig. 1). :3. The dry weight of thatch increased as an exponentially equation in alt :3 varieties of Kentucky blue-grass(Fig. 2). Thatch increased rate(TIR) can used to estimate the specifying a quantity of thatch accumulation from the turf. Thatch increase rate equation as follows. where TH$_2$ is the dry weightof thatch at T$_2$ survey time and TH$_1$ is the dry weight of thatch at $TH_1$ is the dry weight of thatch at $T_1$ survey time. $TIR(mg/cm^2/day)=\frac{Ln\;TH_2 - Ln\; TH_1}{T_2 - T_1}$ 4. Correlation coefficients between the dry weight of thatch and leaf weight was -0.633(P>0.05), and number of tiller of tillers was -0.666(P>0.5), respectively. It means that thatch accumu-lation increased with growth depression of leaf and stem.