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. [24] as the generalized Cayley metric and the block permutation metric have the same magnitude. From the mathematical point of view, the block permutation metric is not natural as the last pair $(n,1)$ is not included in the characteristic set. In this paper, by including $(n,1)$ in the characteristic set, we introduce a new metric that is called cyclic block permutation metric. Under this new metric, we introduce a class of codes that are called cyclic block permutation codes. Based on some techniques from algebraic function fields originated in [21], we give an algebraic-geometric construction of cyclic block permutation codes with reasonably good parameters. By observing a trivial relation between cyclic block permutation metric and block permutation metric, we produce non-systematic codes in block permutation metric that improve all known results given in [24],[23]. More importantly, based on our non-systematic codes, we provide an explicit and systematic construction of block permutation codes which improves the systematic result shown in [24]. In the end, we demonstrate that our cyclic block permutation codes indeed have reasonably good parameters by showing that our construction beats the Gilbert-Varshamov bound.

翻译：由于各种应用,对不同的应用,不同应用都非常关注变异代码。对于不同的应用,一种需要不同度量下的变异代码。通用的Cayley指标由Chee和Vu[4] 采用,而这一指标包括了其他几个特例。然而,通用的Cayley指标一般不容易计算。因此,杨等人(24)采用了块变异指标,因为通用的Cayley指标和区块变异指标具有同等规模。从数学角度看,区块变异参数不是自然的,因为最后一对(n,1)美元没有列入特征集。在本文件中,将(n,1)美元纳入通用的Cayley指标包括若干其他特例。然而,通用的Cayley指标并非一般容易计算。因此,Yang等人(Yang等人)采用了块变异种标准。根据一些变异位函数字段的技术,我们从[21]开始,我们给出了一次变异位数的变异位参数,我们给出了一张变异位数的变变异参数,我们用不固定的变异代码 显示一个不固定的正态代码,我们每个标准的校正的校正的校正的校正的校正结果显示了我们每个的校正的校正的校正的校正结果。