Non-affine Families of 8 x 8 Complex Hadamard Matrices

TL;DR

This paper introduces six new non-affine 3-parameter families of complex Hadamard matrices of order 8, expanding the known classifications by deriving them from algebraic varieties defined by palindromic polynomials.

Contribution

It presents novel non-affine families of 8x8 complex Hadamard matrices that are not equivalent to previously known matrices, derived from algebraic varieties.

Findings

Six new non-affine 3-parameter families of complex Hadamard matrices of order 8.

Families are derived from unimodular points of algebraic varieties defined by palindromic polynomials.

The matrices are explicitly constructed as solutions to polynomial systems ensuring unimodularity.

Abstract

Six non-affine 3-parameter families of complex Hadamard matrices of order 8 are presented. These families contain Hadamard matrices that are not equivalent to any previously known Hadamard matrices in the literature. Each family arises from unimodular points of an affine variety defined by palindromic polynomials. The families are given as an image of a function that solves the corresponding system of polynomials on a domain that guarantees unimodularity of the solutions