Journal of the
Korean Mathematical Society JKMS

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

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).