We explicitly construct an irreducible four-dimensional unitary representation of the Lie group SU (2) and use it for the construction of high-rate unitary space-time codes for four transmit antennas. The tools we use are invariant integration on the group to unitarize the representation, and dense spherical codes on the three-dimensional sphere. Our construction calls for the design of such spherical codes in which the angle between any two points is well separated from 120 degrees. We give a partial solution to this restricted design problem and use numerical optimization techniques to optimize our solution. 1 Introduction It is well-known that multiple antenna links promise very high data rates at very low error probabilities [1, 2]. The theory is in a rather satisfactory level for xed wireless links in which the fading channel coecients are known to the sender and the receiver. However, for mobile applications in which the channel changes very rapidly the situation is far less u...