Quantum Codes from Linear Codes over Finite Chain Rings

Abstract

In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings. The second construction is derived from the CSS construction applied to Gray images of the linear codes over finite chain ring ${\mathbb{F}}_{p^{2m}}+u{\mathbb{F}}_{p^{2m}}$. The good parameters of quantum codes from cyclic codes over finite chain rings are obtained.

References in corpus (1)

• Simple Quantum Error Correcting Codes