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Quaternary complex Hadamard matrices of order 18
Author(s) -
Östergård Patric R. J.,
Paavola William T.
Publication year - 2021
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21760
Subject(s) - hadamard transform , mathematics , complex hadamard matrix , hadamard's maximal determinant problem , hadamard matrix , hadamard's inequality , equivalence (formal languages) , combinatorics , order (exchange) , hadamard three lines theorem , type (biology) , matrix (chemical analysis) , pure mathematics , mathematical analysis , geology , materials science , finance , economics , composite material , paleontology
Abstract A 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) 32 × 32 Hadamard matrices, where the search is split into parts according to matrix types. A classification of the 18 × 18 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.