一类量子负循环码的构造

Construction of a class of quantum negacyclic codes

文章研究了有限域F_(q)^(2)上长为(q^(4)-1)/8的负循环Bose-Chaudhuri-Hocquenghem(BCH)码,其中q为奇素数幂且q≡1(mod 4);给出了厄米特对偶包含负循环BCH码的最大设计距离,并确定了它们的维数;利用厄米特构造法,得到了新的参数良好的量子码。

This paper studies negacyclic Bose-Chaudhuri-Hocquenghem(BCH)codes over the finite field F_(q)^(2)of length(q^(4)-1)/8,where q is an odd prime power and q≡1(mod 4);the maximum designed distance of Hermitian dual-containing negacyclic BCH codes is given and the dimension of these codes is determined;a new class of quantum codes with good parameters is constructed using the Hermitian construction.