arXiv subjects

Vlad Zaitsev

Publications and source records attributed to Vlad Zaitsev.

2 recordsLinked to original sources

arXiv2026

A class of skew-regular quaternary Hadamard matrices

This paper introduces and investigates a novel class of skew-regular Quaternary Hadamard matrices. For every odd prime power $p$, we establish the existence of these matrices for all orders $1+p^2$, each characterized by a constant row sum of $1-pi$. Motivated by the growing importance of large-excess matrices in the maximum determinant problem and quantum nonlocality, we demonstrate that this class provides a robust framework for generating Hadamard matrices with exceptionally large excess.

math.CO↗

arXiv2021

On a class of optimal constant weight ternary codes

A weighing matrix $W$ of order $n=\frac{p^{m+1}-1}{p-1}$ and weight $p^m$ is constructed and shown that the rows of $W$ and $-W$ form optimal constant weight ternary codes of length $n$, weight $p^m$ and minimum distance $p^{m-1}(\frac{p+3}{2})$ for each odd prime power $p$ and integer $m\ge 1$ and thus $$A_3\left(\frac{p^{m+1}-1}{p-1},p^{m-1}\big(\frac{p+3}{2}\big),p^{m}\right)=2\big(\frac{p^{m+1}-1}{p-1}\big).$$

math.CO↗