有限非链环上几类常循环码构造量子码

Construction of quantum codes from several classes of constacyclic codes over finite non-chain rings

文章研究有限非链环R=F_(q)+uF_(q)+vF_(q)+uvF_(q)的性质结构,其中u^(2)=u,v^(2)=v,uv=vu,且q=p^(m),p≠3为奇素数,m为正整数;引入一个新的从R到F_(q)^(4)的Gray映射,给出环R上线性码的Gray象为自正交码的条件;证明有限非链环R上几类常循环码可分解成不同循环码和负循环码的组合,并利用其构造量子码,得到在极小距离、维数、码率等参数都有改进的量子码。

In this paper,the properties of the finite non-chain ring R=F_(q)+uF_(q)+vF_(q)+uvF_(q) are studied,where u^(2)=u,v^(2)=v,uv=vu and q=p^(m),p≠3 is a prime,m is a positive integer.A new Gray mapping from R to F_(q)^(4) is introduced.Conditions for linear codes over R to be self-orthogonal are given.It is proved that some classes of constacyclic codes over R can be decomposed into different combinations of cyclic codes and negative cyclic codes.These constacyclic codes are used to construct quantum codes.Some quantum codes whose parameters are improved on minimal distance,dimension and code rate are obtained.