码长为3(q^2-1)的对偶包含BCH码及量子码的构造

Dual Containing BCH Codes of Length n=3(q^2-1)and Construction of Quantum Codes

利用分圆陪集刻划q2-元BCH码包含其Hermitian对偶码的条件,分别在q=3l+1和q=3l+2情况下,改进了码长n=3(q2-1)的非本原Hermitian对偶包含BCH码的最大设计距离的下界,确定出当2≤δ≤δnew时,对偶包含BCH码的参数,并构造出量子BCH码,结论证明:利用该方法构造出的量子BCH码的参数优于已有文献。

Let q =3l＋1and q =3l＋2be prime powers.The maximal designed distances of imprimitive Hermitian dual containing q 2-ary narrow-sense（NS）and non-narrow-sense（NNS）BCH codes of length n=3（q2-1）are determined,and a series of NS and NNS BCH codes are constructed and their parameters are computed.Consequently,two families of q-ary quantum BCH codes are derived from these BCH codes.Some of these quantum BCH codes constructed from NNS BCH codes have better parameters than those quantum BCH codes available in the literature.