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Schmidt, Bernhard

doi:10.1023/a:1008398319853

Cited by 21 publications

(2 citation statements)

References 15 publications

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“…Ito [14,15,16] introduced the concept of Hadamard groups, he showed a relation between Hadamard difference sets and Hadamard groups and he conjectured that the dicyclic group Q 8t is always a Hadamard group. Schmidt [25] verified Ito's conjecture for 1 ≤ t ≤ 46. Flannery [12] proved that the concepts of cocyclic Hadamard matrix and Hadamard group are equivalent.…”

Section: Introductionmentioning

confidence: 75%

On Hadamard full propelinear codes with associated group C_{2t}\times C_2

Bailera¹,

Borges

Rifà³

2021

Advances in Mathematics of Communications

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We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C 2t × C 2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hadamard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by 3 if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order 16.

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Section: Introductionmentioning

confidence: 75%

On Hadamard full propelinear codes with associated group C_{2t}\times C_2

Bailera¹,

Borges

Rifà³

2021

Advances in Mathematics of Communications

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“…(In some older works the Hadamard matrix constructed in this way was itself referred to as a Williamson matrix but we follow modern convention and do not use this terminology.) Williamson matrices are also studied for their elegant mathematical properties and their relationship to other mathematical conjectures (Schmidt, 1999).…”

Section: The Williamson Conjecturementioning

confidence: 99%

Applying computer algebra systems with SAT solvers to the Williamson conjecture

Bright

Kotsireas

2020

Journal of Symbolic Computation

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We employ tools from the fields of symbolic computation and satisfiability checkingnamely, computer algebra systems and SAT solvers-to study the Williamson conjecture from combinatorial design theory and increase the bounds to which Williamson matrices have been enumerated. In particular, we completely enumerate all Williamson matrices of even order up to and including 70 which gives us deeper insight into the behaviour and distribution of Williamson matrices. We find that, in contrast to the case when the order is odd, Williamson matrices of even order are quite plentiful and exist in every even order up to and including 70. As a consequence of this and a new construction for 8-Williamson matrices we construct 8-Williamson matrices in all odd orders up to and including 35. We additionally enumerate all Williamson matrices whose orders are divisible by 3 and less than 70, finding one previously unknown set of Williamson matrices of order 63.

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2020

Hadamard Matrices

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Untitled

Cited by 21 publications

References 15 publications

On Hadamard full propelinear codes with associated group C_{2t}\times C_2

On Hadamard full propelinear codes with associated group C_{2t}\times C_2

Applying computer algebra systems with SAT solvers to the Williamson conjecture

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