• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.255-270
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• 2020

We studied the MDS self-dual codes over finite chain rings. We stated the projection and lifting of codes over the finite chain rings with respect to the MDS self-dual codes, and then we applied the results to the MDS self-dual codes over Galois rings.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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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.

• Korean Journal of Logic
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• v.10 no.1
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• pp.1-23
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• 2007

Dunn investigated algebras and semantics for negations in non-classical logics. This paper extends his investigation to dual negations, more exactly to duals to the negations in Dunn [3, 5]. I first survey and systematize the algebras of dual negations, i.e., (self-dual) subminimal negation, dual Galois negations, dual minimal negation, wB (or dual intuitionistic) negation, (self-dual) De Morgan negation, and (self-dual) ortho negation, based on partially ordered sets. I next provide dual-perp semantics for these (dual) negations. I finally give representations for them by using dual-perp semantics.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1111-1122
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• 2017

In this work, we consider constacyclic and cyclic self-dual codes over the rings $R_k$. We start with theoretical existence results for constacyclic and cyclic self-dual codes of any length over $R_k$ and then construct cyclic self-dual codes over $R_1={\mathbb{F}}_2+u{\mathbb{F}}_2$ of even lengths from lifts of binary cyclic self-dual codes. We classify all free cyclic self-dual codes over $R_1$ of even lengths for which non-trivial such codes exist. In particular we demonstrate that our constructions provide a counter example to a claim made by Batoul et al. in [1] and we explain why their claim fails.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.821-827
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• 2012

In this paper, we prove that for all odd prime powers $q$ there exist MDS(maximum distance separable) self-dual codes over $\mathbb{F}_{q^2}$ for all even lengths up to $q+1$. Additionally, we prove that there exist MDS self-dual codes of length four over $\mathbb{F}_q$ for all $q$ > 2, $q{\neq}5$.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.211-219
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• 2022

We study MDS(maximum distance separable) self-dual codes over Galois ring R = GR(2^m, r). We prove that there exists an MDS self-dual code over R of length n if (n - 1) divides (2^r - 1), and 2^m divides n. We also provide the current state of the problem for the existence of MDS self-dual codes over Galois rings.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.751-764
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• 2016

We investigate the self-dual codes over Galois rings and determine the mass formula for self-dual codes over Galois rings $GR(p^2,2)$.

• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.217-225
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• 2006

We consider the nonrelativistic limit for the radial solutions to the self-dual equations in the self-dual Abelian Chern-Simons model. We achieve the limit by fixing the common maximum value of solutions.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.915-923
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• 2015

Self-dual codes have been actively studied because of their connections with other mathematical areas including t-designs, invariant theory, group theory, lattices, and modular forms. We presented the building-up construction for self-dual codes over GF(q) with $q{\equiv}1$ (mod 4), and over other certain rings (see [19], [20]). Since then, the existence of the building-up construction for the open case over GF(q) with $q=p^r{\equiv}3$ (mod 4) with an odd prime p satisfying $p{\equiv}3$ (mod 4) with r odd has not been solved. In this paper, we answer it positively by presenting the building-up construction explicitly. As examples, we present new optimal self-dual [16, 8, 7] codes over GF(7) and new self-dual codes over GF(7) with the best known parameters [24, 12, 9].