Rank metric and codes

Rank metric which was introduced by E. M. Gabidulin in 1985, is a new metric thathave found applications in error ? correcting. Since error ? correcting capability of acode depends on the distance between codewords, choosing a convenient metric is considerably important. Most studies in algebraic coding theory are relative to Hamming metric. However this metric is not always suitable for characteristic of channel. Especially if code symbols are elements of higher dimensional Galois field, this incompatiblity is more significant. As Hamming distance cannot distinguish thelinear dependency among the various signals of alphabet, it is inappropriate to criss ? cross errors occurrence. Because of the fact that rank metric capacity of handling varied error patterns efficiently, it is an ideal metric. In this context, firstly finite fields are represented for research in rank metric. In the following part, coding theory is represented in detailed. In the last part, rank metric is represented and codes on the rank metric are researched.