Butson Hadamard Matrices from Pairs of Gauss Sums

@misc{ong2026butson,
  title = {{Butson Hadamard Matrices from Pairs of Gauss Sums}},
  author = {Cheng Yiin Ong and Bernhard Schmidt},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22754},
  eprint = {2609.22754},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22754},
}

TY  - UNPB
TI  - Butson Hadamard Matrices from Pairs of Gauss Sums
AU  - Cheng Yiin Ong
AU  - Bernhard Schmidt
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22754
UR  - https://arxiv.org/abs/2609.22754
AB  - Let q be a prime power. We give a construction of Butson Hadamard matrices BH((F_q× 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× 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.
ER  -