# Journal of theKorean Mathematical SocietyJKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

## Article

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J. Korean Math. Soc. 2022; 59(1): 193-204

Published online January 1, 2022 https://doi.org/10.4134/JKMS.j210357

## Construction for self-orthogonal codes over a certain non-chain Frobenius ring

Boran Kim

Kyungpook National University

### Abstract

We present construction methods for free self-orthogonal (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