On Marrero`s $J_m$-Hadamard matrices

Abstract

Following O. Marrero`s idea [Exposition. Math. 17 (1999), no. 3, 283–287; MR1706192], the authors define a J m -Hadamard matrix to be one of the form \n(M⊗J∣ ∣ ∣ A 1 ⋮A m ), \nwhere M is a Hadamard matrix of order m , J is the t×1 matrix of all ones, and each A i is a t×(mt−m) matrix in which each entry is either 1 or −1 . The authors construct a number of additional J m -Hadamard matrices by permuting and negating the A i `s. They then extend a result of R. Craigen [Ars Combin. 33 (1992), 57–64; MR1174830] to J m -Hadamard matrices. Finally, they introduce the J m -class CJ m of Hadamard matrices and prove that CJ 8 ⊂CJ 4 ⊂CJ