Construction for self-orthogonal codes over a certain non-chain Frobenius ring
J. Korean Math. Soc. 2022 Vol. 59, No. 1, 193-204
https://doi.org/10.4134/JKMS.j210357
Published online November 25, 2021
Printed January 1, 2022
Boran Kim
Kyungpook National University
Abstract : We present construction methods for free self-orthogonal \linebreak (self-dual or Type II) codes over $\mathbb Z_4[v]/\langle v^2+2v \rangle$ which is one of the finite commutative local non-chain Frobenius rings of order $16$. By considering their Gray images on $\mathbb Z_4$, we give a construct method for a code over $\mathbb Z_4$. We have some new and optimal codes over $\mathbb Z_4$ with respect to the minimum Lee weight or minimum Euclidean weight.
Keywords : Frobenius ring, non-chain ring, self-orthogonal code, code over $\mathbb Z_4$, optimal code
MSC numbers : Primary 94B05
Supported by : Boran Kim is supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(NRF-2021R1C1C2012517).
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