• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.341-357
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• 2018

We examine various dualities over the fields of even orders, giving new dualities for additive codes. We relate the MacWilliams relations and the duals of ${\mathbb{F}}_{2^{2s}}$ codes for these various dualities. We study self-dual codes with respect to these dualities and prove that any subgroup of order $2^s$ of the additive group is a self-dual code with respect to some duality.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.703-715
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• 2021

There are several methods for constructing self-dual codes. Among them, the building-up construction is a powerful method. Recently, Kim and Choi proposed special building-up constructions which use symmetric generator matrices for self-dual codes over GF(q), where q is odd. In this paper, we study the same method when q is even.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.193-204
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• 2022

We present construction methods for free self-orthogonal (self-dual or Type II) codes over ℤ₄[v]/〈v² + 2v〉 which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on ℤ₄, we give a construct method for a code over ℤ₄. We have some new and optimal codes over ℤ₄ with respect to the minimum Lee weight or minimum Euclidean weight.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.379-388
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• 2017

Self-dual codes of lengths less than 5 over ${\mathbb{Z}}_p$ are completely classified by the second author [The classification of self-dual modular codes, Finite Fields Appl. 17 (2011), 442-460]. The number of such self-dual codes are also determined. In this article we will extend the results to classify self-dual codes over ${\mathbb{Z}}_{p^2}$ of length less than 5 and give the number of codes in each class. Explicit and complete classifications for small p's are also given.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.285-294
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• 2020

We study the complementary information set codes (for short, CIS codes) over 𝔽₄. They are strongly connected to correlation-immune functions over 𝔽₄. Also the class of CIS codes includes the self-dual codes. We find a construction method of CIS codes over 𝔽₄ and a criterion for checking equivalence of CIS codes over 𝔽₄. We complete the classification of all inequivalent CIS codes of length up to 8 over 𝔽₄.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.729-740
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• 2018

In this paper, we define near-minimal shadow and study the existence problem of extremal Type I additive self-dual codes over GF(4) with near-minimal shadow. We prove that there is no such codes if the code length n = 6m+1($m{\geq}0$), $n=6m+5(m{\geq}1)$.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.965-989
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• 2015

Let p, ${\ell}$ be distinct odd primes, q be an odd prime power with gcd(q, p) = gcd(q,${\ell}$) = 1, and m, n be positive integers. In this paper, we determine all self-dual, self-orthogonal and complementary-dual negacyclic codes of length $2p^{n{\ell}m}$ over the finite field ${\mathbb{F}}_q$ with q elements. We also illustrate our results with some examples.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.525-532
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• 2012

We study the extended quadratic residue code of length 24 over $\mathbb{Z}_3$ and its lifts to rings $\mathbb{Z}_{3^e}$ for all e including 3-adic integers ring. We completely determine the weight enumerators of all these lifts.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.49 no.8
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• pp.55-62
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• 2012

The development of memory design and process technology enabled the production of high density memory. As the weight of embedded memory within aggregate Systems-On-Chips(SoC) gradually increases to 80-90% of the number of total transistors, the importance of testing embedded dual-port memories in SoC increases. This paper proposes a new micro-code based programmable memory Built-In Self-Test(PMBIST) architecture for dual-port memories that support test various test algorithms. In addition, various test algorithms including March based algorithms and dual-port memory test algorithms are efficiently programmed through the proposed algorithm instruction set. This PMBIST has an optimized hardware overhead, since test algorithm can be implemented with the minimum bits by the optimized algorithm instructions.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.131-150
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• 2019

In this paper, we consider the structure of ${\gamma}$-constacyclic codes of length $2p^s$ over the Galois ring $GR(p^a,m)$ for any unit ${\gamma}$ of the form ${\xi}_0+p{\xi}_1+p^2z$, where $z{\in}GR(p^a,m)$ and ${\xi}_0$, ${\xi}_1$ are nonzero elements of the set ${\mathcal{T}}(p,m)$. Here ${\mathcal{T}}(p,m)$ denotes a complete set of representatives of the cosets ${\frac{GR(p^a,m)}{pGR(p^a,m)}}={\mathbb{F}}p^m$ in $GR(p^a,m)$. When ${\gamma}$ is not a square, the rings ${\mathcal{R}}_p(a,m,{\gamma})=\frac{GR(p^a,m)[x]}{{\langle}x^2p^s-{\gamma}{\rangle}}$ is a chain ring with maximal ideal ${\langle}x^2-{\delta}{\rangle}$, where ${\delta}p^s={\xi}_0$, and the number of codewords of ${\gamma}$-constacyclic code are provided. Furthermore, the self-orthogonal and self-dual ${\gamma}$-constacyclic codes of length $2p^s$ over $GR(p^a,m)$ are also established. Finally, we determine the Rosenbloom-Tsfasman (RT) distances and weight distributions of all such codes.