In this paper, we present a new construction of asymmetric quantum codes (AQCs) by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs) which have the following three advantages. First, only the outer codes in AQCTPCs need to satisfy the orthogonal constraint in quantum codes, and any classical linear code can be used for the inner, which makes AQCTPCs very easy to construct. Second, most AQCTPCs are highly degenerate, which means they can correct many more errors than their classical TPC counterparts. Consequently, we construct several families of AQCs with better parameters than known results in the literature. Third, AQCTPCs can be efficiently decoded although they are degenerate, provided that the inner and outer codes are efficiently decodable. In particular, we significantly reduce the inner decoding complexity of TPCs from $\Omega(n_2a^{n_1})(a>1)$ to $O(n_2)$ by considering error degeneracy, where $n_1$ and $n_2$ are the block length of the inner code and the outer code, respectively. Furthermore, we generalize our concatenation scheme by using the generalized CCs and TPCs correspondingly.
翻译:在本文中,我们展示了一种非对称量量代码的新构建,将经典混合代码(CDC)与古典高价产品代码(TPC)(TPC)相结合,称为非对称量聚合代码(AQCTPC)和高价产品代码(AQCTPC),这有三个优点。首先,只有AQCTPC的外部代码需要满足量代码的正反调限制,而且任何古典线性代码都可以用于内部,这使得AQCTPC非常容易构建。第二,大多数AQCTPC都高度退化,这意味着它们能够纠正比传统的高价产品代码(TPC)多得多的错误。因此,我们建造了若干AQC的家族,其参数比文献中已知的结果要好。第三,AQCTPC的外部代码可以有效解码,尽管它们已经退化,但前提是内值和外值代码能够有效地变小。特别是,我们大大降低了TPC的内分解复杂性,从美元(n_a_n__1}(a>1)美元,这意味着它们可以纠正很多错误。