基于多项式码的量子码的构造

Construction of quantum codes based on polynomial

构造量子码的方法有很多,但通过经典线性码构造量子码是最常用的一种构造方法.最近,研究者们利用某类多项式码来构造q元量子码,但是所构造的q元量子码的码长有一定的局限性,文章放宽限制条件,利用这类多项式构造新的参数的经典线性码,然后利用厄米特的自正交性构造出一类量子码.对给定的q,文章所构造的量子码扩大了码长的取值范围.

There are many methods to construct quantum codes, and the classical linear codes of quantum codes is one of them. Recently, many researchers through a construct the classical linear codes certain class of polyno- mials. But there are some limitation with the length of codes. In this paper we loosen the restriction and use these polynomials to construct classical linear codes with new parameters. Then we use the Hermitian self orthog- onal to construct a class of quantum codes. For a given q, the structure of the quantum code expands the range of code length.