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 -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 Hadamard matrices of order and Hadamard matrices of order . These matrices are not necessary different. As a result we obtain a Hadamard matrix of order . 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}
}