论文标题
具有各种船体尺寸和纠缠辅助QECC的二进制最佳线性代码
Binary optimal linear codes with various hull dimensions and entanglement-assisted QECC
论文作者
论文摘要
线性代码$ c $的船体是$ c $与双重的交点。据我们所知，除了自动执行代码外，二进制线性代码的结构很少。我们提出了一个建筑结构，以获取带有船体尺寸$ \ ell，\ ell +1 $的二进制$ [n +2，k +1] $代码，或从给定的二进制$ [n，k] $ code带有船体尺寸$ \ ell $的$ \ ell +2 $。特别是，在船体尺寸1和2方面，我们构建了所有二进制最佳$ [n，k] $长度的代码，最高可达13。在船体尺寸3、4和5方面，我们构建了所有二进制二进制最佳$ [n，k] $长度的代码，直至12，最大可能的最小距离为$ [13，k] $ [13，k] $代码$ 3 $ $ k 3 $ k.作为一个应用程序，我们将二进制最佳代码与给定的船体维度应用于构造几个纠缠辅助量子误差校正校正代码（EAQECC）的二进制最佳代码（EAQECC）。
The hull of a linear code $C$ is the intersection of $C$ with its dual. To the best of our knowledge, there are very few constructions of binary linear codes with the hull dimension $\ge 2$ except for self-orthogonal codes. We propose a building-up construction to obtain a plenty of binary $[n+2, k+1]$ codes with hull dimension $\ell, \ell +1$, or $\ell +2$ from a given binary $[n,k]$ code with hull dimension $\ell$. In particular, with respect to hull dimensions 1 and 2, we construct all binary optimal $[n, k]$ codes of lengths up to 13. With respect to hull dimensions 3, 4, and 5, we construct all binary optimal $[n,k]$ codes of lengths up to 12 and the best possible minimum distances of $[13,k]$ codes for $3 \le k \le 10$. As an application, we apply our binary optimal codes with a given hull dimension to construct several entanglement-assisted quantum error-correcting codes(EAQECC) with the best known parameters.
