# Technical Program

## Paper Detail

 Paper ID A.4.1 Paper Title Improved efficiency for covering codes matching the sphere-covering bound Authors Aditya Potukuchi, Rutgers, The State University of New Jersey, United States; Yihan Zhang, The Chinese University of Hong Kong, China Session A.4: Combinatorial Coding Theory I Presentation Lecture Track Algebraic and Combinatorial Coding Theory Manuscript Click here to download the manuscript Virtual Presentation Click here to watch in the Virtual Symposium Abstract A covering code is a subset $\mathcal{C} \subseteq \{0,1\}^n$ with the property that any $z \in \{0,1\}^n$ is close to some $c \in \mathcal{C}$ in Hamming distance. For every $\epsilon,\delta>0$, we show a construction of a family of codes with relative covering radius $\delta + \epsilon$ and rate $1 - \ent(\delta)$ with block length at most $\exp(O((1/\epsilon) \log (1/\epsilon)))$ for every $\epsilon > 0$. This improves upon a folklore construction which only guaranteed codes of block length $\exp(1/\epsilon^2)$. The main idea behind this proof is to find a distribution on codes with relatively small support such that most of these codes have good covering properties.