Semidefinite programming bounds for codes in complex projective space

Abstract

We establish three-point bounds for codes in complex projective space, where previously only two-point linear programming bounds were known. We discuss how these bounds can be computed numerically using semidefinite programming, and provide a framework that allows for proofs of universal optimality through solving finitely many semidefinite programs. We present some numerical computations that demonstrate, in some test examples, that our three-point bounds improve upon two-point bounds.