We consider the problem of efficiently constructing an as large as possible family of permutations such that each pair of permutations are far part (i.e., disagree on a constant fraction of their inputs). Specifically, for every n ∈ ℕ, we present a collection of N = N(n) = (n!)^Ω(1) pairwise far apart permutations {π_i: [n] → [n]}_i∈[N] and a polynomial-time algorithm that on input i ∈ [N] outputs an explicit description of π_i.

From a coding theoretic perspective, we construct permutation codes of constant relative distance and constant rate along with efficient encoding (and decoding) algorithms. This construction is easily extended to produce constant composition codes on smaller alphabets, where in these codes every codeword is balanced; namely, each symbol appears the same number of times.

Our construction combines routing on the Shuffle-Exchange network with any good binary error correcting code. Specifically, we uses codewords of a good binary code in order to determine the switching instructions in the Shuffle-Exchange network.

我们考虑有效构建尽可能大的排列族的问题，使得每对排列都是远部分（即，在其输入的恒定分数上不一致）。具体来说，对于每个n ε ℕ，我们提出N = N ( n ) = ( n !) ^Ω(1)成对相距较远的排列 { π _i : [ n ] → [ n ]} _{i ∈[ N ]}的集合，并且一种多项式时间算法，根据输入i ∈ [ N ] 输出π _i的显式描述。

从编码理论的角度来看，我们构造了恒定相对距离和恒定速率的排列码以及高效的编码（和解码）算法。这种结构很容易扩展以在较小的字母表上生成恒定的组合代码，其中在这些代码中每个码字都是平衡的；即每个符号出现的次数相同。

我们的构造将 Shuffle-Exchange 网络上的路由与任何良好的二进制纠错代码结合起来。具体来说，我们使用良好的二进制代码的码字来确定Shuffle-Exchange网络中的切换指令。