# Algorithmic Aspects on the Construction of Separating Codes

• Marcel Fernandez
• John Livieratos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11544)

## Abstract

In this paper, we discuss algorithmic aspects of separating codes, that is, codes where any two subsets (of a specified size) of their code words have at least one position with distinct elements. More precisely we focus on the (non trivial) case of binary 2-separating codes. Firstly, we use the Lovász Local Lemma to obtain a lower bound on the existence of such codes that matches the previously best known lower bound. Then, we use the algorithmic version of the Lovász Local Lemma to construct such codes and discuss its implications regarding computational complexity. Finally, we obtain explicit separating codes, with computational complexity polynomial in the length of the code and with rate larger than the well-known Simplex code.

## Keywords

Separating codes Lovász Local Lemma Moser-Tardos constructive proof

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## Authors and Affiliations

• Marcel Fernandez
• 1
• John Livieratos
• 2
1. 1.Department of Network EngineeringUniversitat Politecnica de CatalunyaBarcelonaSpain
2. 2.Department of MathematicsNational and Kapodistrian University of AthensAthensGreece