4 research outputs found
A simple construction of complex equiangular lines
A set of vectors of equal norm in represents equiangular lines
if the magnitudes of the inner product of every pair of distinct vectors in the
set are equal. The maximum size of such a set is , and it is conjectured
that sets of this maximum size exist in for every . We
describe a new construction for maximum-sized sets of equiangular lines,
exposing a previously unrecognized connection with Hadamard matrices. The
construction produces a maximum-sized set of equiangular lines in dimensions 2,
3 and 8.Comment: 11 pages; minor revisions and comments added in section 1 describing
a link to previously known results; correction to Theorem 1 and updates to
reference