Quaternary complex Hadamard matrices of order 18

Abstract

AbstractA technique for classifying Butson‐type Hadamard matrices over the complex 4th roots of unity is developed. The technique resembles the approach used by Kharaghani and Tayfeh‐Rezaie in their classification of the (real) Hadamard matrices, where the search is split into parts according to matrix types. A classification of the Butson‐type Hadamard matrices over the complex 4th roots of unity is carried out; the number of such objects up to Hadamard equivalence is 1 955 625.