Counting results for thin Butson matrices

Teo Banica¹

¹Cergy-Pontoise University

The electronic journal of combinatorics, Tome 21 (2014) no. 3

Résumé

A partial Butson matrix is a matrix $H\in M_{M\times N}(\mathbb Z_q)$ having its rows pairwise orthogonal, where $\mathbb Z_q\subset\mathbb C^\times$ is the group of $q$-th roots of unity. We investigate here the counting problem for these matrices in the "thin" regime, where $M=2,3,\ldots$ is small, and where $N\to\infty$ (subject to the condition $N\in p\mathbb N$ when $q=p^k>2$). The proofs are inspired from the de Launey-Levin and Richmond-Shallit counting results.

Détail

DOI : 10.37236/3891

Classification : 05B20, 05A15
Mots-clés : Hadamard matrix, Butson matrix