Corpus ID: 219179425

Formal Orthogonal Pairs via Monomial Representations and Cohomology

@article{Goldberger2020FormalOP,
  title={Formal Orthogonal Pairs via Monomial Representations and Cohomology},
  author={Assaf Goldberger and I. Kotsireas},
  journal={arXiv: Combinatorics},
  year={2020}
}
A Formal Orthogonal Pair is a pair $(A,B)$ of symbolic rectangular matrices such that $AB^T=0$. It can be applied for the construction of Hadamard and Weighing matrices. In this paper we introduce a systematic way for constructing such pairs. Our method involves Representation Theory and Group Cohomology. The orthogonality property is a consequence of non-vanishing maps between certain cohomology groups. This construction has strong connections to the theory of Association Schemes and (weighted… Expand

References

SHOWING 1-10 OF 21 REFERENCES
Homological models for semidirect products of finitely generated Abelian groups
Algebraic Design Theory
Gröbner bases and cocyclic Hadamard matrices
The cocyclic Hadamard matrices of order less than 40
Geometriae Dedicata
The Magma Algebra System I: The User Language
Hadamard matrices and their applications: Progress 2007–2010
  • K. Horadam
  • Mathematics, Computer Science
  • Cryptography and Communications
  • 2010
Hadamard Matrices and Their Applications
"J."
...
1
2
3
...