On Codes Identifying Sets of Vertices in Hamming Spaces

Authors:
Iiro Honkala;Tero Laihonen;Sanna Ranto
Affiliations:
Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland;Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland;Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland
Venue:
Designs, Codes and Cryptography
Year:
2001

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Abstract

A code C \subseteq F_2^n is called (t,{\leq} 2)-identifying if for all the words x, y(x\ne y) and z the sets (B_{t}(x)\cup B_{t}(y))\cap C and B_{t}(z)\cap C are nonempty and different. Constructions of such codes and a lower bound on the cardinality of these codes are given. The lower bound is shown to be sharp in some cases. We also discuss a more general notion of (t,\mathcal{F})-identifying codes and introduce weakly identifying codes.