Bernhard Schmidt

collaborators

5 papers

math.CO2026

Butson Hadamard Matrices from Pairs of Gauss Sums

Cheng Yiin Ong, Bernhard Schmidt

Let $q$ be a prime power. We give a construction of Butson Hadamard matrices $B H ((F_{q} \times F_{q}, +), l c m (6, d))$ for any divisor $d > 1$ of $q - 1$ . Most character values of the group rin…

math.CO2026

A Family of Gauss Type Hadamard Difference Sets

Bernhard Schmidt

A Hadamard difference set (HDS) $D$ of order $u^{2}$ in an abelian group $G$ satisfies $∣ χ (D) ∣ = u$ for every nontrivial character $χ$ of $G$ . We call such a character value naive if i…

math.NT2019

Upper Bounds for Cyclotomic Numbers

Tai Do Duc, Ka Hin Leung, Bernhard Schmidt

Let $q$ be a power of a prime $p$ , let $k$ be a nontrivial divisor of $q - 1$ and write $e = (q - 1) / k$ . We study upper bounds for cyclotomic numbers $(a, b)$ of order $e$ over the finite…

math.CO2019

Bilinear Forms on Finite Abelian Groups and Group-Invariant Butson Hadamard Matrices

Tai Do Duc, Bernhard Schmidt

Let $K$ be a finite abelian group and let $exp (K)$ denote the least common multiple of the orders of the elements of $K$ . A $B H (K, h)$ matrix is a $K$ -invariant $∣ K ∣ \times ∣ K ∣$ mat…