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

What the study found: The study presents six non-affine 3-parameter families of complex Hadamard matrices of order 8. These families include Hadamard matrices that are not equivalent to any previously known matrices in the literature.
Why the authors say this matters: The authors say these families expand the known collection of complex Hadamard matrices. They also note that the families contain matrices not equivalent to earlier examples.
What the researchers tested: The researchers worked with unimodular points, meaning points whose values have magnitude 1, of an affine variety defined by palindromic polynomials. The families are given as the image of a function that solves the corresponding system of polynomials on a domain chosen to guarantee unimodularity of the solutions.
What worked and what didn't: The approach produced six non-affine 3-parameter families of order-8 complex Hadamard matrices. The abstract states that some matrices in these families are not equivalent to any previously known Hadamard matrices, but it does not describe any unsuccessful cases.
What to keep in mind: The available summary does not describe limitations, comparisons in detail, or broader consequences beyond the stated existence of the new families.

Key points

• Six non-affine 3-parameter families of complex Hadamard matrices of order 8 were presented.
• Some matrices in these families are not equivalent to any previously known Hadamard matrices in the literature.
• The families arise from unimodular points of an affine variety defined by palindromic polynomials.
• The families are given as the image of a function that solves a system of polynomials on a domain guaranteeing unimodularity.
• The abstract does not describe limitations or unsuccessful constructions.