In this report, one of the properties of rank distance code (RD) which is the surface area of rank sphere is discussed .It is showed that the kth surface area Sk (0), which is the collection of rank norm-k is distance invariant and the weight distributions of the translatesSk(x) ofSk(O) are the same for all xE Sc (0). Ultimately, the weight distribution of Sk{x )when llx II= 1 is determined.

A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics