On the twin designs with the Ionin-type parameters

H. Kharaghani

The electronic journal of combinatorics, Tome 7 (2000)

Résumé

Let $4n^2$ be the order of a Bush-type Hadamard matrix with $q=(2n-1)^2$ a prime power. It is shown that there is a weighing matrix $$ W(4(q^m+q^{m-1}+\cdots+q+1)n^2,4q^mn^2) $$ which includes two symmetric designs with the Ionin–type parameters $$ \nu=4(q^m+q^{m-1}+\cdots+q+1)n^2,\;\;\; \kappa=q^m(2n^2-n), \;\;\; \lambda=q^m(n^2-n) $$ for every positive integer $m$. Noting that Bush–type Hadamard matrices of order $16n^2$ exist for all $n$ for which an Hadamard matrix of order $4n$ exist, this provides a new class of symmetric designs.

Détail

DOI : 10.37236/1479

Classification : 05B20, 05B05
Mots-clés : symmetric design, regular Hadamard matrix, Bush-type Hadamard matrix, design with Ionin-type parameters, balanced generalized weighing matrix