an:01436245
Zbl 0961.05068
de Launey, Warwick; Stafford, Richard M.
On cocyclic weighing matrices and the regular group actions of certain Paley matrices
EN
Discrete Appl. Math. 102, No. 1-2, 63-101 (2000).
00064417
2000
j
05E20 05B20
weighing matrix; group of automorphisms; regular group actions; Paley matrices
By definition a weighing matrix \(W= W(x,t)\) is an \(n\times n\) matrix with entries in \(\{0,\mp 1\}\) satisfying \(WW^T= W^TW= tI_n\) where \(T\) denotes the transposition and \(I_n\) is the identity matrix of degree \(n\). An automorphism of \(W\) is a pair of signed permutations \((P,Q)\) such that \(PMQ^T= M\), and the set of all automorphisms of \(W\) forms a group which is called the group of automorphisms of \(W\) and is denoted by \(\Aut(W)\). Since Paley conference matrices are weighing matrices a study of the group of automorphisms of such matrices is set up in the paper. The study is also carried out for certain Paley Hadamard matrices. The authors determine all regular group actions obtained from these Paley matrices.
Mohammad-Reza Darafsheh (Tehran)