Constacyclic codes over the ring F-q + vF(q) + v(2)F(q) and their applications of constructing new non-binary quantum codes

摘要

Let R = F-q + vF(q) + v(2)F(q) be a finite non-chain ring, where q is an odd prime power and v(3) = v. In this paper, we propose two methods of constructing quantum codes from (alpha + beta v + gamma v(2))-constacyclic codes over R. The first one is obtained via the Gray map and the Calderbank-Shor-Steane construction from Euclidean dualcontaining (alpha + beta v + gamma v(2))-constacyclic codes over R. The second one is obtained via the Gray map and the Hermitian construction from Hermitian dual-containing (alpha + beta v + gamma v(2))-constacyclic codes over R. As an application, some new non-binary quantum codes are obtained. Let be a finite non-chain ring, where q is an odd prime power and . In this paper, we propose two methods of constructing quantum codes from -constacyclic codes over R. The first one is obtained via the Gray map and the Calderbank-Shor-Steane construction from Euclidean dual-containing (alpha + beta v + gamma v(2))-constacyclic codes over R. The second one is obtained via the Gray map and the Hermitian construction from Hermitian dual-containing (alpha + beta v + gamma v(2))-constacyclic codes over R. As an application, some new non-binary quantum codes are obtained.