Permutation codes have received a great attention due to various applications. For different applications, one needs permutation codes under different metrics. The generalized Cayley metric was introduced by Chee and Vu [4] and this metric includes several other metrics as special cases. However, the generalized Cayley metric is not easily computable in general. Therefore the block permutation metric was introduced by Yang et al. [22] as the generalized Cayley metric and the block permutation metric have the same magnitude. However, the block permutation metric lacks the symmetry property which restricts more advanced algebraic tools to be involved. In this paper, by introducing a novel metric closely related to the block permutation metric, we build a bridge between some advanced algebraic methods and codes in the block permutation metric. More specifically, based on some techniques from algebraic function fields originated in [19], we give an algebraic-geometric construction of codes in the novel metric with reasonably good parameters. By observing a trivial relation between the novel metric and block permutation metric, we then produce non-systematic codes in block permutation metric that improve all known results given in [21, 22]. More importantly, based on our non-systematic codes, we provide an explicit and systematic construction of codes in block permutation metric which improves the systematic result shown in [22]. In the end, we demonstrate that our codes in the novel metric itself have reasonably good parameters by showing that our construction beats the corresponding Gilbert-Varshamov bound.

翻译：由于各种应用,对不同的应用,对不同的应用,有一个需要不同度量下的变异代码。通用的Cayley测量标准由Chee和Vu[4]采用,而这一测量标准包括了其他几个特殊指标。然而,通用的Cayley测量标准一般不容易进行可比较。因此,杨等人(22)采用了块变异标准,因为通用的Cayley测量标准和块变异测量标准具有同等规模。但是,对于不同的应用,区块变异指标缺乏限制更先进的变异工具参与的对称属性。在本文件中,通过引入与块变异衡量标准密切相关的新颖的Cayley测量标准,我们在一些先进的变异计量方法和块变异指标编码之间搭建了一座桥梁。更具体地说,由于杨等人等人(Yang等人)的变异位函数领域的某些技术,我们用比较好的比值来构建新度标准。通过观察新版的衡量指标和区块变异参数之间的微关系,我们随后在系统化的建筑标准中 展示了一种非系统化的校正的校正的校正代码,我们以系统化的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正结果。我们以显示了我们所的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正的校正结果。