Author

Minjia Shi

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Preprint Oct 2026

Double circulant LCD codes over $\mathbb{F}_2+u\mathbb{F}_2$ and constructions for binary LCD codes

Linear complementary dual (LCD) codes are linear codes that intersect their dual trivially. We study double circulant (Euclidean) LCD codes over the finite chain ring $R=\mathbb F_2+u\mathbb F_2$, where $u^2=0$. Using the Chinese Remainder Theorem and the factorization of $x^n-1$, we derive an explicit enumeration form...

Xing-Xing Xu, Min-Jia Shi, Jon-Lark Kim · 0 citations

Jul 2026

Cyclic codes and cyclically covering subspaces

A subspace of $\mathbb{F}_q^n$ is called cyclically covering if the union of $\sigma^i(U)$ can cover the whole space $\mathbb{F}_q^n$, where $\sigma$ is the cyclic shift, $0 \leqslant i \leqslant n-1$. Let $h_q(n)$ be the largest possible co-dimension of a cyclically covering subspace of $\mathbb{F}_q^n$. We show that...

Xuan Wang, Minjia Shi · arXiv.org · 0 citations