This paper investigates the construction and analysis of permutation codes under the Chebyshev distance. The direct product group permutation (DPGP) codes, introduced independently by Kl\o ve et al. and Tamo et al., represent the best-known permutation codes in terms of both size and minimum distance. These codes possess algebraic structures that facilitate efficient encoding and decoding algorithms. In particular, this study focuses on recursively extended permutation (REP) codes, which were also introduced by Kl\o ve et al. We examine the properties of REP codes and prove that, in terms of size and minimum distance, the optimal REP code is equivalent to the DPGP codes. Furthermore, we present efficient encoding and decoding algorithms for REP codes.

翻译：本文研究了切比雪夫距离下置换码的构造与分析。由Kløve等人与Tamo等人分别独立提出的直积群置换码，在码本规模和最小距离方面代表了目前已知最优的置换码。这些码具有便于高效编码与解码算法实现的代数结构。本研究特别关注同样由Kløve等人提出的递归扩展置换码。我们分析了递归扩展置换码的性质，并证明在码本规模和最小距离方面，最优的递归扩展置换码等价于直积群置换码。此外，我们提出了针对递归扩展置换码的高效编码与解码算法。