Reversible Cyclic Codes over F2+uF2+u2F2

Reversible cyclic codes over Z4

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.

On cyclic codes and quasi-cyclic codes over Zq + uZq

Let R = Zq + uZq, where q = p and u = 0. In this paper, some structural properties of cyclic codes and quasi-cyclic (QC) codes over the ring R are considered. A QC code of length ln with index l over R is viewed both as in the conventional row circulant form and also as an R[x]/(x − 1)-submodule of GR(R, l)[x]/(x − 1), where GR(R, l) is the Galois extension ring of degree l over R. A necessary ...

Cyclic Codes and Self-Dual Codes Over

We introduce linear cyclic codes over the ring F 2 + uF 2 = f0; 1; u; u = u + 1g, where u = 0 and study them by analogy with the Z4 case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z4-codes. Unlike the Z4 case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-d...

$\Theta_S-$cyclic codes over $A_k$

We study ΘS−cyclic codes over the family of rings Ak. We characterize ΘS−cyclic codes in terms of their binary images. A family of Hermitian inner-products is defined and we prove that if a code is ΘS−cyclic then its Hermitian dual is also ΘS−cyclic. Finally, we give constructions of ΘS−cyclic codes. ∗Corresponding author. email: [email protected]