论文标题
相对船体和量子代码
Relative hulls and quantum codes
论文作者
论文摘要
给定两个$ q $ - 元代码$ C_1 $和$ C_2 $，相对于$ C_2 $的相对船体为$ C_1 $是交叉点$ C_1 \ CAP C_2^\ PERP $。我们证明，当$ q> 2 $时，可以通过用同等的两个代码替换两个代码中的任何一个，将相对船体尺寸重复降低到一定限制。相对船体尺寸的缩小适用于相对于$ e $ galois内部产品采取的船体，该产品具有特殊情况，同时具有Euclidean和Hermitian Inner Products。我们提供的条件在$ q> 2 $时，可以通过等效代码增加相对船体维度。我们研究了相对船体特性对纠缠量子误差校正代码的一些后果，并证明存在新的纠缠量符合量子误差的最大距离代码，这意味着那些参数满足量子singletleton结合的距离。
Given two $q$-ary codes $C_1$ and $C_2$, the relative hull of $C_1$ with respect to $C_2$ is the intersection $C_1\cap C_2^\perp$. We prove that when $q>2$, the relative hull dimension can be repeatedly reduced by one, down to a certain bound, by replacing either of the two codes with an equivalent one. The reduction of the relative hull dimension applies to hulls taken with respect to the $e$-Galois inner product, which has as special cases both the Euclidean and Hermitian inner products. We give conditions under which the relative hull dimension can be increased by one via equivalent codes when $q>2$. We study some consequences of the relative hull properties on entanglement-assisted quantum error-correcting codes and prove the existence of new entanglement-assisted quantum error-correcting maximum distance separable codes, meaning those whose parameters satisfy the quantum Singleton bound.
