Bilinear forms on finite abelian groups and group-invariant Butson Hadamard matrices

Duc, Tai Do; Schmidt, Bernhard

doi:10.1016/j.jcta.2019.03.002

Cited by 5 publications

(4 citation statements)

References 15 publications

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“…In Table 2 we recall the distribution of matrices per classes of BH(n, q) in the said database. (5,5), BH(6, 3), BH (6,4), BH (6,6), BH (7,6), BH (7,7), BH (8,2), BH (8,8), BH(9, 3), BH (9,6), BH (9,9), BH (9,10), BH (10,4), BH (10,10), BH (11,11), BH (12,2), BH (12,3), BH (12,12), BH (12,36), BH (13,13), BH(13, 60)…”

Section: Numerical Resultsmentioning

confidence: 99%

“…for all (a 1 , a 2 ) ∈ Z r q and hence the matrix H defined in ( 4) is Z r q -group invariant in the sense of [8]. Note that the matrix defined in (3) is not Z r q -group invariant.…”

Section: Fourier Transformsmentioning

confidence: 99%

“…Remark 6.2. The condition in Theorem 6.1 is necessary but not sufficient as BH (8,4) contains two matrices neither leading to self-dual bent sequences. Still, 8 = 2 2 + 2 2 , with y 0 = 4, y 1 = y 2 = 2, y 3 = 0.…”

Section: Existence Conditionsmentioning

confidence: 99%

“…General constructions of Butson Hadamard matrices with designed self-dual bent sequences are then derived from, respectively, Kronecker products of Butson matrices, regular Butson matrices, Bush type Hadamard matrices, and generalized Walsh Hadamard matrices. In the last case we use group invariant Butson matrices in the sense of [8,22]. Strong necessary existence conditions for Butson matrices admitting self-dual bent sequences with trivial multiplier are given.…”

Section: Introductionmentioning

confidence: 99%

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Hadamard bent sequences-survey and new results

Shi¹,

Xiao²,

Solé³

2022

Preprint

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A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application (Solé et al, 2021). The subclass of self-dual bent sequences was studied from the standpoint of generation and symmetry (Shi et al., 2022). An analogous study was led for complex Hadamard matrices (Shi et al., submitted). We survey these recent results, and add some new results (asymptotics, Mutually Unbiased Hadamard matrices). MSC (2020): 05B20, 94D10, 94B25

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Section: Numerical Resultsmentioning

confidence: 99%

“…for all (a 1 , a 2 ) ∈ Z r q and hence the matrix H defined in ( 4) is Z r q -group invariant in the sense of [8]. Note that the matrix defined in (3) is not Z r q -group invariant.…”

Section: Fourier Transformsmentioning

confidence: 99%

Section: Existence Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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