Combinatorial constructions of separating codes

Abstract

This paper presents an algorithmic approach to the construction of separating codes. In the first part of the work, the Lovász Local Lemma is used to obtain a lower bound on the code rate. This lower bound matches the previously best-known lower bound. In the second part, it is shown how the technique used in proving the lower bound leads to an algorithm that outputs an instance of a separating code. Moreover, the implications of the algorithm regarding computational complexity are considered. The discussion ends by presenting explicit separating codes with polynomial computational complexity in the length of the code, with rate that improves previously known constructions.