The equivalence between optimal detecting arrays and super-simple OAs

Authors:
Ce Shi;Yu Tang;Jianxing Yin
Affiliations:
Department of Mathematics, Soochow University, Suzhou, China 215006;Department of Mathematics, Soochow University, Suzhou, China 215006;Department of Mathematics, Soochow University, Suzhou, China 215006
Venue:
Designs, Codes and Cryptography
Year:
2012

Citing 3
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Abstract

The notion of a detecting array (DTA) was proposed, recently, by Colbourn and McClary in their research on software interaction tests. Roughly speaking, testing with a (d, t)驴DTA(N, k, v) can locate d interaction faults and detect whether there are more than d interaction faults. In this paper, we establish a general lower bound on sizes of DTAs and explore an equivalence between optimal DTAs and super-simple orthogonal arrays (OAs). Taking advantage of this equivalence, a great number of DTAs are constructed, which are all optimal in the sense of their sizes. In particular, an optimal (2, t)驴DTA(N, 5, v) of strength t = 2 or 3 is shown to exist whenever v 驴 3 excepting $${(t, v) \in \{(2, 3), (2, 6),(3, 4), (3, 6)\}}$$ .