基于经典线性码构造的纠缠辅助量子码

Entanglement-Assisted Quantum CodesConstructed by Classical Linear Codes

首先,利用有限域F_(q)上参数为[n,k,d]经典线性码C的线性互补对偶(LCD)线性子码的一个正交基,构造一类参数为[[n+l,k-h,d′;n-k-h+l]]的纠缠辅助量子码,其中h=dim(Hull_(E)(C)),0≤l≤k-h,d≤d′≤d+l.特别地,当经典线性码C为Euclide对偶包含线性码时,存在一个参数为[[n+l,2k-n,d′;l]]的纠缠辅助量子码,其中0≤l≤2k-n,d≤d′≤d+l.其次,通过对有限域F_(q)上参数为[n,k,d]的Euclide对偶包含线性码C的校验矩阵H作一类变换,构造另一类参数为[[n+l,2k-n+l,d′;2l]]的纠缠辅助量子码,其中0≤l≤n-k,d≤d′≤d+l.

Firstly,a class of entanglement-assisted quantum codes with parameters[[n+l,k-h,d′;n-k-h+l]]are constructed by using an orthogonal basis of the linear complementary dual(LCD)linear subcode of the classical linear code C with parameters[n,k,d]over a finite field F_(q),where h=dim(Hull_(E)(C)),0≤l≤k-h,d≤d′≤d+l.In particular,when the classical linear code C is Euclidean dual-containing linear code,there are entanglement-assisted quantum codes with parameters[[n+l,2k-n,d′;l]],where 0≤l≤2k-n,d≤d′≤d+l.Secondly,by making a kind of transformation on the parity check matrix H of Euclidean dual-containing linear code C with parameters[n,k,d],another kind of entanglement-assisted quantum codes with parameters[[n+l,2k-n+l,d′;2l]]are constructed,in which 0≤l≤n-k,d≤d′≤d+l.