Cyclic codes and comparison of codes in finite

The thesis defines a new type of two-variable ring. Cyclic, constacyclic, quasicyclic code definitions are presented on this ring type and propositions comparing the relationships between them are given. In the first part of the thesis, the first studies in coding theory, the research in the literature with its development are mentioned. In the second part, the basic algebraic concepts required especially for linear and cyclic codes within the scope of coding theory are given. In the third part, the ring with the conditions 𝑢1 3 = 0, 𝑢2 3 = 0 and 𝑢1 ∙ 𝑢2 = 𝑢2 ∙ 𝑢1 = 0 and the two-variable coefficients in 𝔽2 are given. The quasi-cyclic codes corresponding to the constacyclic codes in this ring in the object 𝔽2 are examined. In the fourth section, cyclic codes in two-variable rings with coefficients in 𝔽3 and 𝔽𝑝 are discussed with the conditions 𝑢1 3 = 0, 𝑢2 3 = 0 and 𝑢1 ∙ 𝑢2 = 𝑢2 ∙ 𝑢1 = 0 and the results of their Gray images are examined and interpreted. In the last section, a general conclusion of the first four sections is drawn.