3 years ago

On the List Decodability of Self-orthogonal Rank Metric Codes.

Shu Liu

V. Guruswami and N. Resch prove that the list decodability of $\mathbb{F}_q$-linear rank metric codes is as good as that of random rank metric codes in~\cite{venkat2017}. Due to the potential applications of self-orthogonal rank metric codes, we focus on list decoding of them. In this paper, we prove that with high probability, an $\F_q$-linear self-orthogonal rank metric code over $\mathbb{F}_q^{n\times m}$ of rate $R=(1-\tau)(1-\frac{n}{m}\tau)-\epsilon$ is shown to be list decodable up to fractional radius $\tau\in(0,1)$ and small $\epsilon\in(0,1)$ with list size depending on $\tau$ and $q$ at most $O_{\tau, q}(\frac{1}{\epsilon})$. In addition, we show that an $\mathbb{F}_{q^m}$-linear self-orthogonal rank metric code of rate up to the Gilbert-Varshamov bound is $(\tau n, \exp(O_{\tau, q}(\frac{1}{\epsilon})))$-list decodable.

Publisher URL: http://arxiv.org/abs/1801.07033

DOI: arXiv:1801.07033v1

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.