• 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.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.25-43
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• 2005

Let F be a finite field of prime power order q(odd) and the multiplicative order of q modulo $2^{n}\;(n>1)\;be\; {\phi}(2^{n})/2$. If n > 3, then q is odd number(prime or prime power) of the form $8m{\pm}3$. If q = 8m - 3, then the ring $R_{2^n} = F[x]/ < x^{2^n}-1 >$ has 2n primitive idempotents. The explicit expressions for these primitive idempotents are obtained and the minimal QR cyclic codes of length $2^{n}$ generated by these idempotents are completely described. If q = 8m + 3 then the expressions for the 2n - 1 primitive idempotents of $R_{2^n}$ are obtained. The generating polynomials and the upper bounds of the minimum distance of minimal QR cyclic codes generated by these 2n-1 idempotents are also obtained. The case n = 2,3 is dealt separately.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.27 no.2
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• pp.397-408
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• 2017

As mobile traffic increases rapidly, DMM (Distributed Mobility Management) has been proposed as a mobility management technology for seamless communication of mobile devices as mobile traffic increases rapidly. the DMM distributes mobility management from the core network to the edge network, enabling stable binding updates with low latency. However, the DMM still have network delay and security problems for sessions. In this paper, we point out the problems existing in the DMM and propose a new protocol in which the MN (Mobile Node) directly participates in authentication and mutual authentication is correctly performed to solve this problem. We demonstrate not only security improvements but also performance improvements with performance analysis.