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arXiv · 2609.22754

Butson Hadamard Matrices from Pairs of Gauss Sums

Cheng Yiin Ong·Bernhard Schmidt
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Abstract

Let $q$ be a prime power. We give a construction of Butson Hadamard matrices $BH((F_q\times F_q,+),lcm(6,d))$ for any divisor $d>1$ of $q-1$. Most character values of the group ring elements corresponding to these matrices involve products of two Gauss sums over $F_q$ (with non-quadratic Gauss sums occurring) and this property distinguishes our result from all previously known constructions of group invariant Butson Hadamard matrices. In fact, our $BH((F_q\times F_q,+),lcm(6,d))$ matrices arise as a special case of a more general construction based on what we call ``Butson-Jacobsthal functions'' that resembles the construction of Hadamard matrices from Jacobsthal matrices.

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BibTeXRIS

Cheng Yiin Ong, Bernhard Schmidt. 2026-09-19. Butson Hadamard Matrices from Pairs of Gauss Sums. https://arxiv.org/abs/2609.22754

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