论文标题
具有柔性维度的欧几里得和赫尔米亚人船体的MDS代码及其应用于EAQECCS
MDS Codes with Euclidean and Hermitian Hulls of Flexible Dimensions and Their Applications to EAQECCs
论文作者
论文摘要
线性代码的船体是与某些内部产品相对于其双重代码的交点。欧几里得和赫尔米尼亚船体都具有理论和实践意义。在本文中，我们通过（扩展）广义的Reed-Solomon（GRS）代码构建了几类新的MDS代码，并确定其欧几里得或遗传学船体。具体而言，构建了具有灵活维度的Hermitian船体的四个新类的MDS代码，以及六个具有柔性维度欧几里得船体的新类MDS代码。对于前者，我们进一步构建了四个新类别的纠缠量子误差校正代码（EAQECC）和四个新的MDS EAQECC，长度为$ n> q+1 $。对于后者，我们还提供了一些有关欧几里得自动和一维欧几里得船体MDS代码的例子。
The hull of a linear code is the intersection of itself with its dual code with respect to certain inner product. Both Euclidean and Hermitian hulls are of theorical and practical significance. In this paper, we construct several new classes of MDS codes via (extended) generalized Reed-Solomon (GRS) codes and determine their Euclidean or Hermitian hulls. Specifically, four new classes of MDS codes with Hermitian hulls of flexible dimensions and six new classes of MDS codes with Euclidean hulls of flexible dimensions are constructed. For the former, we further construct four new classes of entanglement-assisted quantum error-correcting codes (EAQECCs) and four new classes of MDS EAQECCs of length $n>q+1$. For the latter, we also give some examples on Euclidean self-orthogonal and one-dimensional Euclidean hull MDS codes.
