量子突发纠错乘积码的构造

Constructions of Quantum Burst-Correcting Product Codes

量子突发纠错码是以CSS量子码的纠错原理和构造技术为基础,在量子计算和量子通信中有着十分重要的作用。首次利用GF(q)上的任意线性码C1=n,k1[,d]1 q和满足对偶包含关系的BCH码C2=n,k2[,d]2 q,来构造乘积码C1C2和(C1C2)⊥,当满足n2>2k1k2时,在CSS构造的基础上便可构造参数为[[n2,n2-n]]的量子突发纠错乘积码,并给出其突发纠错能力。

Quantum burst-correcting codes based on the elegant structure of CSS codes play an important role in quantum computation and quantum communication. Let C1 = [ n, k1, d1 ] q denote an arbitrary linear code and C2 = [ n ,k2 ,d2 ] q be a BCH code over GF（q） C1 and C2 are used for the first time to construct theC1 （×）C2 and （C1 （×）C2）^⊥ product codes. If n2 〉2k1k2, then based on CSS construction, the quantum burst-correcting product codes with parameter [[ n2, n2-n ] ] can be constructed. Moreover, its ability in con-structing the quantum burst-correcting codes is also given.