Notes on Z2Z2[u]-Cyclic Self-Dual and Quantum Codes

Arezoo Soufi Karbaski, Taher Abualrub, Steven T. Dougherty

Minjia Shi, Liqin Qian, Yan Liu +1 more

Shivanshu Benjwal, Maheshanand Bhaintwal

İsmail Aydoğdu, Taher Abualrub

In this paper we introduce self-dual cyclic and quantum codes over Z2^α x (Z2 + uZ2)^β. We determine the conditions for any Z2Z2[u]-cyclic code to be self-dual, that is, C = C^{\perp}. Since the binary image of a self-orthogonal Z2Z2[u]-linear code is also a self-orthogonal binary linear code, we introduce quantum codes over Z2^α x (Z2 + uZ2)^β. Finally, we present some examples of self-dual cyclic and quantum codes that have good parameters.

İsmail Aydoğdu, Taher Abualrub

In this paper, we introduce self-dual cyclic codes over the ring [Formula: see text]. We determine the conditions for any [Formula: see text]-cyclic code to be self-dual, that is, [Formula: see text]. Since the binary image of a self-orthogonal [Formula: see text]-linear code is also a self-orthogonal binary linear code, we introduce quantum codes over [Formula: see text]. Finally, we present some examples of self-dual cyclic and quantum codes that have good parameters.

Chaofeng Guan, Ruihu Li, Liangdong Lü +2 more