Applying balanced generalized weighing matrices to construct block designs

Yury J. Ionin

The electronic journal of combinatorics, Tome 8 (2001) no. 1

Résumé

Balanced generalized weighing matrices are applied for constructing a family of symmetric designs with parameters $(1+qr(r^{m+1}-1)/(r-1),r^{m},r^{m-1}(r-1)/q)$, where $m$ is any positive integer and $q$ and $r=(q^{d}-1)/(q-1)$ are prime powers, and a family of non-embeddable quasi-residual $2-((r+1)(r^{m+1}-1)/(r-1),r^{m}(r+1)/2,r^{m}(r-1)/2)$ designs, where $m$ is any positive integer and $r=2^{d}-1$, $3\cdot 2^{d}-1$ or $5\cdot 2^{d}-1$ is a prime power, $r\geq 11$.

Détail

DOI : 10.37236/1556

Classification : 05B05, 05B20
Mots-clés : non-embeddable quasi-residual designs, non-embeddability, symmetric design, balanced generalized weighing matrices