An Elementary Condition for Non-Norm Elements

Abstract—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 or HEX, which is easier to check. With this elementary condition, non-norm elements with smaller absolute values than the existing ones can be found. Index Terms—Algebraic number theory, cyclic division algebra, non-norm elements, nonvanishing determinant, space–time block codes. I