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arXiv · 1309.1851

On generalized Hadamard matrices GH(q,q)'s and GH(q,q^2)'s

Hiroaki Kido
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Abstract

A matrix $H=[d_{ij}]$ is a generalized Hadamard matrix of order $uλ$ with entries from $U$ which is a finite group of order $u$ (for short $\mathrm{GH}(u,\,λ)$) such that whenever $i\neq \ell$ the set $\{d_{ij}d_{\ell j}^{-1}\,|\, 1\leq j\leq uλ\}$ contains each element of $U$ exactly $λ$ times. In this paper, we construct $\mathrm{GH}(q,\,q)$'s and $\mathrm{GH}(q,\,q^{2})$'s over additive groups of finite fields $\mathrm{GF}(q)$'s by using some sorts of functions.

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Hiroaki Kido. 2013-09-07. On generalized Hadamard matrices GH(q,q)'s and GH(q,q^2)'s. https://arxiv.org/abs/1309.1851

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