有限域上的本原量子BCH码
Primitive Quantum BCH Codes over Finite Fields
摘要：
BCH码的一个吸引人的特征是，人们可以从它们的设计参数（长度、有限域的大小和设计距离）中推断出有价值的信息，例如码的最小距离和维数的界限。在本文中，它表明，人们也可以推断出的设计参数是否原始的，狭义BCH包含其欧几里德或厄米特对偶码。这些信息在量子BCH码的构造中是非常宝贵的。给出了小设计距离BCH码的维数的一个新的证明，并由此导出了这类码的最小距离和码长的简单界。这些结果使我们能够得到两个家庭的原始量子BCH码的参数作为其设计参数的函数。
英文摘要：
An attractive feature of BCH codes is that one can infer valuable information from their design parameters (length, size of the finite field, and designed distance), such as bounds on the minimum distance and dimension of the code. In this paper, it is shown that one can also deduce from the design parameters whether or not a primitive, narrow-sense BCH contains its Euclidean or Hermitian dual code. This information is invaluable in the construction of quantum BCH codes. A new proof is provided for the dimension of BCH codes with small designed distance, and simple bounds on the minimum distance of such codes and their duals are derived as a consequence. These results allow us to derive the parameters of two families of primitive quantum BCH codes as a function of their design parameters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
