Reversible DNA codes from skew cyclic codes over a ring of order 256

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.

Reversible cyclic codes over Z4

On cyclic DNA codes over the Ring $\Z_4 + u \Z_4$

In this paper, we study the theory for constructing DNA cyclic codes of odd length over Z4[u]/〈u 2〉 which play an important role in DNA computing. Cyclic codes of odd length over Z4+uZ4 satisfy the reverse constraint and the reverse-complement constraint are studied in this paper. The structure and existence of such codes are also studied. The paper concludes with some DNA example obtained via ...

From skew-cyclic codes to asymmetric quantum codes

We introduce an additive but not F4-linear map S from Fn4 to F 4 and exhibit some of its interesting structural properties. If C is a linear [n, k, d]4-code, then S(C) is an additive (2n, 2 , 2d)4-code. If C is an additive cyclic code then S(C) is an additive quasi-cyclic code of index 2. Moreover, if C is a module θ-cyclic code, a recently introduced type of code which will be explained below,...

Skew Generalized Quasi-cyclic Codes

This article discusses skew generalized quasi-cyclic codes over any finite field F with Galois automorphism θ. This is a generalization of quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes since their lengths do not have to be multiples of the index. After a brief description of the skew polynomial ring F[x; θ], we show that a skew general...