10.3336/gm Glasnik matematički ISSN 0017-095X (Tisak) ISSN 1846-7989 (Online) Hrvatsko matematičko društvo i PMF-Matematički odsjek Sveučilišta u Zagrebu Bijenička cesta 30, 10000 Zagreb glasnik@math.hr http://web.math.hr/glasnik/ 10.3336/gm.58.2.07 Izvorni znanstveni članak Bush-type Butson Hadamard matrices Kharaghani Hadi kharaghani@uleth.ca 1 Pender Thomas tsp7@sfu.ca 2 Land Caleb Van't caleb.vantland@uleth.ca 3 Zaitsev Vlad vlad.zaitsev@uleth.ca 4 Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge AB T1K 3M4, Canada Department of Mathematics, University of Simon Fraser, Burnaby BC V5A 1S6, Canada Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge AB T1K 3M4, Canada Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge AB T1K 3M4, Canada 27 12 2023 Vol 58 Svezak 2 247 257

Bush-type Butson Hadamard matrices are introduced. It is shown that a nonextendable set of mutually unbiased Butson Hadamard matrices is obtained by adding a specific Butson Hadamard matrix to a set of mutually unbiased Bush-type Butson Hadamard matrices. A class of symmetric Bush-type Butson Hadamard matrices over the group \(G\) of \(n\)-th roots of unity is introduced that is also valid over any subgroup of \(G\). The case of Bush-type Butson Hadamard matrices of even order will be discussed.

 Hadamard matrix, unbiased Hadamard matrix, Bush-type Hadamard matrix