In this paper, we discuss a method to construct an equidistant rank metric code for any metric. Then we study properties of rank metric codes. The size of the constructed code is a power of2. It also shown that, if C is the constructed code, then C+C is an equidistant constant-weight code. The highlight of the paper is that the kernel of the code C happens to be an equidistant constant- weight code of the same size as C. Finally, the construction of equidistant rank metric code does not depend on the choice of metric.

A Dissertation Submitted in partial fulfillment of the requirements for the degree of Master of Science in mathematics