A simple construction of cover-free $(s,\ell)$-code with certain constant weight

TL;DR

This paper presents a straightforward method to construct cover-free (s, l)-codes with constant weight, useful in combinatorial group testing and related applications.

Contribution

The authors introduce a new construction technique for cover-free (s, l)-codes that guarantees constant column weight, expanding the toolkit for combinatorial designs.

Findings

Constructs cover-free (s, l)-codes with specific parameters

Achieves codes with constant column weight

Provides a method applicable for various values of n, s, l

Abstract

We give a method of constructing a cover-free $(s, \ell)$-code. For $k > s$, our construction yields a $ {{n \choose s} \choose \ell}\times {n \choose k}$ cover-free $(s, \ell)$-code with a constant column weight.