An Elementary Condition for Non-norm Elements for QAM and HEX Signals

Cyclic division algebra (CDA) has recently become a major technique to construct space-time block codes with nonvanishing determinant (NVD). One of the key steps in this technique is the determination of non-norm elements and a sufficient condition for the determination has been given by Kiran and Rajan lately based on algebraic number theory. In this paper, based on Kiran and Rajan´s condition, we present a more elementary condition for non-norm elements when signals are QAM, i.e., in Z[i], or HEX, i.e., Z[j], which is easier to check. With this elementary condition, non-norm elements with smaller absolute values than the existing ones can be found.