一种2^(m)元域上量子纠错码的构造方法

A Construction Method of Quantum Error-correcting Codes over F_(2m)

构造具有良好参数的量子码是量子纠错码研究的重要内容。该文利用有限非链环R=F_(4m)+vF_(4m)上的厄米特对偶包含常循环码来构造2^(m)元量子码。定义了一种新的Gray映射φ,能够将环R上线性码C的厄米特对偶包含性保持到φ(C)上。研究了环R上常循环码是厄米特对偶包含码的条件。给出了一种构造2m元量子码的方法,并构造了一些新的4元和8元量子码。

Constructing quantum codes with good parameters is an important part of quantum error-correcting codes research.In this paper,2^(m)-ary quantum codes are derived through Hermitian dual-containing constacyclic codes over finite non-chain ring R=F_(4m)+vF_(4m).A new Gray mapφis defined,which is Hermitian dual-containing preserving from a linear code C over R toφ(C).The condition for constacyclic codes over R to be Hermitian dual-containing is studied.A method of constructing 2^(m)-ary quantum codes is presented,and some new 4-ary and 8-ary quantum codes are obtained.