Quaternary complex Hadamard matrices of order 18

Östergård, Patric R. J.; Paavola, William T.

doi:10.1002/jcd.21760

Cited by 1 publication

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“…In the literature, studies of equivalence of Butson-type Hadamard matrices over mth roots of unity have mainly considered the case m = 4; see [13,14]. We have |Aut(C 4 )| = 2, and the only nontrivial element corresponds to complex conjugation.…”

Section: Definitionmentioning

confidence: 99%

“…Hadamard and related matrices are considered in this paper; for more information about such structures, [2,4,7] can be consulted. See also [8,9,[11][12][13][14] for specific classi-B Patric R. J. Östergård patric.ostergard@aalto.fi 1 Department of Communications and Networking, Aalto University School of Electrical Engineering, P.O. Box 15400, 00076 Aalto, Finland fication studies.…”

Section: Introductionmentioning

confidence: 99%

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Equivalence of Butson-type Hadamard matrices

Östergård

2022

J Algebr Comb

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Two matrices $$H_1$$ H 1 and $$H_2$$ H 2 with entries from a multiplicative group G are said to be monomially equivalent, denoted by $$H_1\cong H_2$$ H 1 ≅ H 2 , if one of the matrices can be obtained from the other via a sequence of row and column permutations and, respectively, left- and right-multiplication of rows and columns with elements from G. One may further define matrices to be Hadamard equivalent if $$H_1 \cong \phi (H_2)$$ H 1 ≅ ϕ ( H 2 ) for some $$\phi \in \mathrm {Aut}(G)$$ ϕ ∈ Aut ( G ) . For many classes of Hadamard and related matrices, it is straightforward to show that these are closed under Hadamard equivalence. It is here shown that also the set of Butson-type Hadamard matrices is closed under Hadamard equivalence.

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Section: Definitionmentioning

confidence: 99%