We study linear unitary precoding for multiple antenna transmissions. Our aim is to find a new precoder satisfying both the genie conditions and the non-vanishing determinant criterion. Such a precoder will be optimized for both maximum likelihood and iterative probabilistic decoding. By combining the rank criterion and the genie conditions, we propose a new family of space-time codes over [i] defined by Pythagorean triples. In this family, the space-time code associated with the triple (3,4,5) - or with the quaternion algebra - is optimal. We will refer to it as Aladdin-Pythagoras, or more simply, Aladdin's Code. 2010 Lavoisier, Paris.
