English

On Sylvester-type constructions of Hadamard matrices and their modifications

Combinatorics 2022-11-02 v1

Abstract

Using the ideas of concatenation construction of codes over the qq-ary alphabet, we modify the known generalized Sylvester-type construction of the Hadamard matrices. The new construction is based on two collections of the Hadamard matrices. In particular this construction involves mm Hadamard matrices of order kk and kk Hadamard matrices of order mm. These matrices are not necessary different. As a result we obtain a Hadamard matrix of order kmkm. The new construction gives many possibilities for construction of the new Hadamard matrices with different ranks and dimension of kernel.

Keywords

Cite

@article{arxiv.2211.00160,
  title  = {On Sylvester-type constructions of Hadamard matrices and their modifications},
  author = {Dmitrii Zinoviev and Victor Zinoviev},
  journal= {arXiv preprint arXiv:2211.00160},
  year   = {2022}
}