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, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.

In this work, cyclic-skew-cyclic codes and sum-rank BCH are introduced. Cyclic-skew-cyclic characterized as left ideals of a suitable non-commutative finite ring, constructed using skew polynomials on top (or vice versa). Single generators such found, they used to construct generator matrices the corresponding codes. The notion defining set is introduced, pairs roots poynomials. A lower bound (...

Prompted by a question of Jim Propp, this paper examines the cyclic sieving phenomenon (CSP) in certain codes. For example, it is shown that, among dual Hamming codes over Fq, generating function for codedwords according to major index statistic (resp. inversion statistic) gives rise CSP when q=2 or q=3 q=2). A byproduct curious characterization irreducible polynomials F2[x] and F3[x] that are ...

‎‎a natural generalization of two dimensional cyclic code ($t{tdc}$) is two dimensional skew cyclic code‎. ‎it is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $r_n:=f[x,y;rho,theta]/_l$‎. ‎in this paper we characterize the left ideals of the ring $r_n$ with two methods and find the generator matrix for two dimensional s...