IJPAM: Volume 16, No. 2 (2004)

MODIFYING A PARITY-CHECK MATRIX
TO A SEPARABLE MATRIX

J.Y. Guo$^1$, F.K. Hwang$^2$
$^{1,2}$Department of Applied Mathematics
National Chiao Tung University
1001 Ta Hsueh Road, Hsinchu, 300, TAIWAN, R.O.C.
$^1$e-mail: davidguo@math.nctu.edu.tw
$^2$e-mail: fhwang@math.nctu.edu.tw


Abstract.The $\overline{d}$-separable matrix $M$ and the transpose of the parity check matrix $H$ of an $e$-error-correcting code satisfy similar requirement, but one is based on Boolean sum, while the other on modulo-2 sum. Consequently, $H$ cannot be used directly as $M$ with $d=e$. Kautz and Singleton [#!KS64!#] gave a method to modify $H$ with $e=2$. They suggested that the method can be extended to $e=3$. In this paper, we give such a method for the $\overline{3}$-separable matrix. We also discuss some result for $e=4$.

Received: July 1, 2004

AMS Subject Classification: 15A30

Key Words and Phrases: parity-check, separable, group testing, nonadaptive

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 2