PG(k-1,4)中的自正交cap和量子纠错码的构造

Self-orthogonal caps in PG(k-1,4) and construction quantum codes

目的构造量子纠错码。方法随机试验和组合方法。结果利用随机搜索算法,得到一些PG(k-1,4)中完备且正交的cap,从而构成F4上6个对偶距离为4的自正交码。结论构造出具有较好参数的自正交码和量子纠错码,改进了已有量子纠错码的参数。

Aim To investigate the method of constructing quantum error-correcting code by self-orthogonal cap over PG（k - 1,4）. Methods Using random searching method to find self-orthogonal caps, and using combinatorial method to construct self-orthogonal codes and quantum error-correcting codes. Results A random searching algorithm for complete cap over PG（k - 1,4） is designed, and some complete and self-orthogonal caps over PG（k - 1, 4） are found. By using of these self-orthogonal caps, nine new self-orthogonal codes of dual distance 4 are obtained. Conclusion Some good self-orthogonal codes over F4 and good quantum error-correcting codes are constructed, these codes are better than the previously known.