Minjia Shi

Skew Cyclic Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$

2015 · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

In this article, we study skew cyclic codes over $R=\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and v3=v. We describe the generator polynomials of skew cyclic codes over this ring and investigate the structural …

Three-weight codes and the quintic construction

2016 · arXiv (Cornell University)

We construct a class of three-Lee-weight and two infinite families of five-Lee-weight codes over the ring $R=\mathbb{F}_2 +v\mathbb{F}_2 +v^2\mathbb{F}_2 +v^3\mathbb{F}_2 +v^4\mathbb{F}_2,$ where $v^5=1.$ The same ring occurs in the quintic construction of binary quasi-cyclic codes. …

On self-dual four circulant codes

2017 · arXiv (Cornell University)

Four circulant codes form a special class of $2$-generator, index $4$, quasi-cyclic codes. Under some conditions on their generator matrices they can be shown to be self-dual. Artin primitive root conjecture shows the existence of …

Optimal quaternary linear codes with one-dimensional Hermitian hull and the related EAQECCs

2022 · arXiv (Cornell University)

Linear codes with small hulls over finite fields have been extensively studied due to their practical applications in computational complexity and information protection. In this paper, we develop a general method to determine the exact …

Expanding self-orthogonal codes over a ring $\Z_4$ to self-dual codes and unimodular lattices

2024 · arXiv (Cornell University)

Self-dual codes have been studied actively because they are connected with mathematical structures including block designs and lattices and have practical applications in quantum error-correcting codes and secret sharing schemes. Nevertheless, there has been less …