• 충청수학회지
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• 제33권2호
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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.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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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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• 제4권3_4호
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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.

• 충청수학회지
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• 제36권3호
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• pp.181-194
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• 2023

Let GR(2^m, r) be a Galois ring with even characteristic. We are interested in the existence of MDS(Maximum Distance Separable) self-dual codes over GR(2^m, r). In this paper, we prove that there exists an MDS self-dual code over GR(2^m, r) with parameters [n, n/2, n/2 + 1] if (n - 1) | (2^r - 1) and 8 | n.