Two applications of separating systems to nonadaptive procedures

✍ Scribed by Anthony J. Macula

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 297 KB
• Volume: 169
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(96)00091-x

✦ Synopsis

Let [n] denote {1,2 ..... n}. A set system tr on [n] is called a separating system on In] if for each pair of distinct elements in In], there is an M E a that contains exactly one member of that pair. A separatin9 system ~ on In] is called totally separating if for each pair of distinct elements j, j' in [hi, there are disjoint M,M' E r with j E M and j' E M'. In this paper, we discuss two applications of separating systems. In the first application, we give an easy method of constructing a class of single error-correcting double error-detecting codes over an Abelian group alphabet. In the second application, we construct a class of 3-separable matrices. Separable matrices are important notions in the theories of nonadaptive group testing and binary superimposed codes.