Linear codes over quaternion rings

In recent years, Algebraic Coding Theory has attracted many researchers due to the increase of digital information transfer and storage. The message sent due to any noise that may occur in the channel during this transfer or storage is subject to change. For this reason, the error occurs and the received message becomes different from the one sent. The Coding Theory or the Error Correcting Codes Theory deals with correcting these errors to the best of their ability, correcting errors correctly. This interdisciplinary field study, which is associated with many subdivisions of mathematics, was first conducted by Shannon in 1948. In the following many studies, coding theory has been studied on different algebraic structures such as fields, rings. Initially, studies on finite fields were first generalized to rings by Hammons et al. [4]. Quaternions were first introduced by Hamilton in 1847. This structure, which allows dividing two vectors, has attracted many mathematicians. In recent years, researchers working in the field of coding theory have given the construction of linear codes and many more code families, called quaternion integers, coefficients on integers, and developed decoding techniques. In this thesis, the ring of quaternions with coefficients from called finite quaternions ring has been studied. It has been shown that the ring, first of all algebraic properties, is a finite, non commutative and non chain ring. Codes have been worked on the module of the elements of this ring. Linear codes are constructed on this structure and the parameters are determined by giving the generator matrix to the standard form. Moreover, cyclic codes, constacyclic codes and polycyclic codes have been studied and parameters have been given for these codes.