On the Cyclic Codes over F 3 + vF 3
نویسنده
چکیده
In this paper, we investigate the structure of cyclic codes over the ring F3 + vF3 where v2 = 1 and F3 = {0, 1, 2}. We prove that cyclic codes over the ring are principally generated, and give the generator polynomial of cyclic codes over this ring. Mathematics Subject Classification: 94B05
منابع مشابه
On Skew Cyclic Codes over a Finite Ring
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.
متن کاملSome notes on the characterization of two dimensional skew cyclic codes
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...
متن کامل2-D skew constacyclic codes over R[x, y; ρ, θ]
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...
متن کاملOn Skew Cyclic and Quasi - cyclic Codes Over F 2 + uF 2 + u 2 F 2
We construct a new Gray map from S to F 3n 2 where S = F2+uF2+uF2, u3 = 1. It is both an isometry and a weight preserving map. It was shown that the Gray image of cyclic code over S is quasi-cyclic codes of index 3 and the Gray image of quasi-cyclic code over S is l-quasi-cyclic code of index 3. Moreover, the skew cyclic and skew quasi-cyclic codes over S introduced and the Gray images of them ...
متن کاملOn Quantum Codes Obtained From Cyclic Codes Over F_2+vF_2+v^2F_2
A new Gray map which is both an isometry and a weight preserving map from R = F2 + vF2 + v 2F2 to F 3 2 is defined. A construction for quantum error correcting codes from cyclic codes over finite ring R = F2 + vF2 + v 2F2, v 3 = v is given.The parameters of quantum codes which are obtained from cyclic codes over R are determined.
متن کامل