In this paper we study Butson Hadamard matrices, and codes over finite rings coming from
these matrices in logarithmic form, called BH-codes. We introduce a new morphism of …

This doctoral thesis covers several topics related to the construction and study of maximal
determinant matrices with complex entries. The first three chapters are devoted to number …

We explore a notion of bent sequence attached to the data consisting of an Hadamard
matrix of order $ n $ defined over the complex $ q^{th} $ roots of unity, an eigenvalue of that …

An $ n\times n $ complex matrix $ M $ with entries in the $ k^{\textrm {th}} $ roots of unity
which satisfies $ MM^{\ast}= nI_ {n} $ is called a Butson Hadamard matrix. While a matrix …

Let G be a finite abelian group and let\exp (G) exp (G) denote the least common multiple of
the orders of all elements of G. A\, BH\,(G, h) BH (G, h) matrix is a G-invariant| G| *| G|| G|×| G …

In a recent survey, Schmidt compiled equivalences between generalized bent functions,
group invariant Butson Hadamard matrices, and abelian splitting relative difference sets. We …

Let G be a finite group and let h be a positive integer. A BH (G, h) matrix is a G-invariant∣
G∣×∣ G∣ matrix H whose entries are complex h th roots of unity such that HH*=∣ G∣ I∣ …

Let a and h be positive integers and let p be a prime. Let q 1,…, qt be the distinct prime
divisors of h and write Q (h)={∑ i= 1 tciqi: ci∈ Z, ci≥ 0}. We provide constructions of group …

Let M be a square matrix of order n and X a vector of n components, each with complex
entries. We are interested in studying MX= X for some particular M where X denotes the …

The purpose of this dissertation is to introduce the reader to the study of group invariant
Butson Hadamard matrices and to present our contribution in this area. Our focus is on …