An significant milestone study in coding theory recognized to be the paper written by Hammons at al. [1]. Fields are useful area for constructing codes but after the study [1] finite ring have received a great deal of attention. Most of the studies are concentrated on the case with codes over finite chain rings. However, optimal codes over nonchain rings exist (e.g see [2].) In [3], et al. stud...

We study prime ideals in skew power series rings T := R[[y; τ, δ]], for suitably conditioned complete right noetherian rings R, automorphisms τ of R, and τ -derivations δ of R. Such rings were introduced by Venjakob, motivated by issues in noncommutative Iwasawa theory. Our main results concern “Cutting Down” and “Lying Over.” In particular, assuming that τ extends to a compatible automorphsim ...

For a finite field $mathbb{F}_q$, the bivariate skew polynomial ring $mathbb{F}_q[x,y;rho,theta]$ has been used to study codes cite{XH}. In this paper, we give some characterizations of the ring $R[x,y;rho,theta]$, where $R$ is a commutative ring. We investigate 2-D skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $R[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ A...

In this paper, using generalized partial skew versions of Armendariz rings, we study the transfer of left (right) zip property between a ring R and partial skew generalized power series rings